BT -0.005 Tc /Length 8 >> /Meta703 718 0 R q Q /BBox [0 0 0.263 0.283] Q /F1 6 0 R >> 0.458 0 0 RG 1 j >> q 45.249 0 0 45.147 217.562 149.056 cm 0 G stream /Matrix [1 0 0 1 0 0] q >> W* n stream q endobj 0000143641 00000 n /Font << /Type /XObject 0 0 l q >> q endstream endstream /Length 55 W* n /FormType 1 /Subtype /Form 467 0 obj << /Meta114 125 0 R /Subtype /Form endobj 0.015 w /Meta615 630 0 R /Type /XObject /Subtype /Form q /Matrix [1 0 0 1 0 0] q 0 0.129 m 0.458 0 0 RG /Font << endstream /Meta769 Do /Meta741 756 0 R endobj Q /Subtype /Form q /Meta519 Do /FormType 1 Q q >> q endobj /Font << 0000286823 00000 n /FormType 1 0 0.087 TD endobj endstream /Meta524 539 0 R /Subtype /Form endstream ET q /Meta68 Do 0.564 G /Meta662 Do [(-)] TJ 0000243713 00000 n /Font << /F1 6 0 R 1.547 0 l /F3 0.217 Tf BT >> 0.015 w With this quiz and worksheet, you'll answer questions designed to test your knowledge of dividing and multiplying complex numbers in polar form. 0 0.087 TD /FormType 1 stream 1 g /XObject << /F1 0.217 Tf 9.523 0 l 0000191218 00000 n 0.458 0 0 RG /Length 51 /F1 0.217 Tf 0 G /Resources << /Resources << /I0 Do /F1 6 0 R /Meta358 371 0 R /Meta539 Do 0.001 Tw 0 0.5 m 0 0.283 m /Length 51 >> [(1)19(5\))] TJ 1 g [(4)] TJ /F1 0.217 Tf 0.564 G /Meta293 306 0 R 0.267 0 l /Subtype /Form 0000153494 00000 n /FormType 1 q endobj stream q /F3 0.217 Tf /Meta857 Do /Matrix [1 0 0 1 0 0] 0 G stream -0.007 Tc 0 0.283 m 0.267 0.283 l endobj /Matrix [1 0 0 1 0 0] >> q q endobj /Meta177 188 0 R 1 g /Meta28 Do 0000141946 00000 n /F1 0.217 Tf 0.564 G q BT q Q Q endstream /Matrix [1 0 0 1 0 0] [(22)] TJ /Length 136 0 0.283 m /Meta1065 Do 0.458 0 0 RG /Meta1039 1056 0 R 0 g >> >> q q 0 0 l Q q /F1 6 0 R W* n /Meta565 580 0 R /Font << 664 0 obj << /F1 0.217 Tf 0000257275 00000 n q >> 0000051450 00000 n q /FormType 1 /Length 102 /Matrix [1 0 0 1 0 0] /Length 69 q /Font << /Length 8 q 578.159 643.654 l /Font << >> /F1 6 0 R /F3 0.217 Tf Q 0 G 10. /Meta154 165 0 R /Resources << 0000100160 00000 n Q /Subtype /Form stream 0000055546 00000 n 0 g /FormType 1 /Meta408 Do Q 0.031 0.087 TD 0000174361 00000 n 0000187687 00000 n 0.015 w /Length 66 /Length 8 Q /Meta61 72 0 R W* n /Length 102 endobj /Meta966 Do /BBox [0 0 9.523 0.283] /Matrix [1 0 0 1 0 0] q q endstream BT stream /FormType 1 /BBox [0 0 0.531 0.283] /Resources << /F1 0.217 Tf 590 0 obj << 227 0 obj << endobj /Meta12 Do /Resources << 0.031 0.158 TD endobj BT /BBox [0 0 1.547 0.283] 0 0 l BT /F1 0.217 Tf /Subtype /Form /Subtype /Form /Length 55 663 0 obj << Q /Meta161 Do >> 45.249 0 0 45.147 329.731 149.056 cm /F1 0.217 Tf 0 0 l BT 0 0 l 0 G endobj /Meta899 914 0 R Q BT 0 G 0.564 G 0 0 l endobj endobj 0000039624 00000 n BT ET 45.249 0 0 45.147 441.9 674.519 cm /Meta500 Do Q /Type /XObject /Length 51 /Meta166 177 0 R /BBox [0 0 1.547 0.633] endstream Plus each one comes with an answer key. >> q endstream /FormType 1 /BBox [0 0 1.547 0.33] 0000091531 00000 n /Subtype /Form /F3 21 0 R Q endobj 401 0 obj << q 0.066 0.087 TD q q /Type /XObject /Meta931 946 0 R 1 g Q /Type /XObject q q 906 0 obj << 0 0.283 m /Subtype /Form /Type /XObject Q /Type /XObject /Resources << BT 0 g ET 0.267 0 l 0.696 0.437 TD q ET /Font << /Meta213 224 0 R Q 0000019970 00000 n [(Add o)-24(r s)-14(u)-19(bt)-26(ract )-25(a)-21(s i)-16(n)-19(dica)-35(ted)-30(. Complex numbers answered questions that for … 0.458 0 0 RG /Subtype /Form /Length 102 0000045957 00000 n /BBox [0 0 1.547 0.633] endstream 753 0 obj << >> stream ET >> 0000060113 00000 n /F1 6 0 R /FormType 1 /BBox [0 0 1.547 0.633] 0 G endobj Q /Matrix [1 0 0 1 0 0] endobj 45.249 0 0 45.131 329.731 216.057 cm 0.015 w Q 45.213 0 0 45.147 36.134 42.91 cm 0000255246 00000 n 0 g Q stream 0 0.633 m 0.314 0.158 TD [(2)] TJ Q >> q 0 G 0000139185 00000 n 0 0 l /Resources << stream 0000001061 00000 n Q 9.523 0 l 0 G Q /Type /XObject 0000154709 00000 n /Matrix [1 0 0 1 0 0] 0 0.283 m q /Font << /Matrix [1 0 0 1 0 0] >> Here we introduce a number (symbol ) i = √-1 or i2 = -1 and we may deduce i3 = -i i4 = 1 45.249 0 0 45.527 441.9 535.249 cm Q Q /Meta146 157 0 R >> 917 0 obj << /F1 0.217 Tf Find N when a = 1000 acres and p = 75 lb/acre. [(-)] TJ q ET 0 0.283 m 45.249 0 0 45.527 217.562 535.249 cm Q 0.283 0.087 TD /FormType 1 /Font << /Subtype /Form /Subtype /Form 0 w /Matrix [1 0 0 1 0 0] 0000246126 00000 n 387 0 obj << /FormType 1 /Subtype /Form >> q 45.249 0 0 45.527 105.393 468.249 cm >> 45.249 0 0 45.131 441.9 143.034 cm 0 g /Meta851 866 0 R /Matrix [1 0 0 1 0 0] q >> /Subtype /Form /Subtype /Form 0 G Q >> Q 45.249 0 0 45.527 329.731 535.249 cm /Meta458 Do stream Q q /Type /XObject /Matrix [1 0 0 1 0 0] 0.417 0.283 l /Font << S q 0 g 1.547 0.283 l 0 0 l /Subtype /Form /Subtype /Form /Meta1064 Do -0.002 Tc >> >> 0 0 l 370 0 obj << -0.003 Tc /Type /XObject 838 0 obj << /FormType 1 [(2)19(6\))] TJ 0.401 0.366 m /Subtype /Form 1095 0 obj << /FormType 1 /Meta624 Do /Meta244 Do endstream Q 1.547 -0.003 l 1 g /F1 0.217 Tf 482 0 obj << 584 0 obj << >> /Matrix [1 0 0 1 0 0] 912 0 obj << /FormType 1 q Q /Meta330 Do /BBox [0 0 0.413 0.283] q Q 0.458 0 0 RG 1 g Q 0 g /FormType 1 2.114 0.087 TD /Subtype /Form 0.031 0.437 TD /Type /XObject >> Q >> q Q 0000273449 00000 n BT /Meta620 Do 1 g >> Q 0 g /Type /XObject q q Q /Type /XObject 45.663 0 0 45.147 90.337 86.573 cm 542.777 99.371 m >> Q 0000060432 00000 n /FormType 1 /Meta171 182 0 R 0000271513 00000 n Q /F3 21 0 R W* n >> q W* n endstream >> 0 g >> /BBox [0 0 9.523 0.283] ET /Font << /Length 51 [(C\))] TJ /Meta904 Do 1.696 0.087 TD Q 0.5 0.087 TD q [(i\))] TJ 45.249 0 0 45.147 105.393 86.573 cm stream 0.564 G /Length 55 endstream 1 J 0000219758 00000 n /Resources << /F1 0.217 Tf 0000288029 00000 n >> /Type /XObject BT /Length 53 0000009687 00000 n >> /Subtype /Form >> ET 0 0.283 m 0.458 0 0 RG /F1 6 0 R 0 G /Matrix [1 0 0 1 0 0] >> /Subtype /Form /Matrix [1 0 0 1 0 0] q q 0 w /Font << /Matrix [1 0 0 1 0 0] /Resources << 0.015 w >> 0 0.283 m 0 0 l 9.791 0.283 l stream 0.232 0.087 TD >> q stream Q W* n /FormType 1 S 0 G 0 0.283 m >> endobj endobj /Resources << 0 g q 45.663 0 0 45.147 314.675 107.652 cm /Length 55 /Subtype /Form 0.564 G S /Subtype /Form stream Q q Q q 0.531 0.437 TD 45.214 0 0 45.131 81.303 244.664 cm q 45.249 0 0 45.147 217.562 368.125 cm /Matrix [1 0 0 1 0 0] Q 0000140645 00000 n /Meta1088 Do endstream for any complex number zand integer n, the nth power zn can be de ned in the usual way (need z6= 0 if n<0); e.g., z 3:= zzz, z0:= 1, z := 1=z3. /Matrix [1 0 0 1 0 0] [(i\)\()] TJ endstream >> q 45.214 0 0 45.147 81.303 691.834 cm 588 0 obj << /Meta434 Do 22) Agriculture: The number of bags of soybean seeds N that a farmer needs varies jointly as the number of acres a to be planted and the pounds of seed needed per acre p, and N = 980 when a = 700 acres and p = 70 lb/acre. Q endstream 45.413 0 0 45.147 523.957 629.351 cm 1 g endstream /F1 6 0 R BT /Meta281 Do stream 0 G stream stream Q 45.214 0 0 45.413 81.303 338.012 cm . /Meta324 Do Q >> Q Q ET q >> stream /FormType 1 Q /FormType 1 >> 0 0 l 1106 0 obj << Q /Font << 0 g 0 g 0000168862 00000 n 0 g /F1 6 0 R W* n /Subtype /Form /FormType 1 /Resources << /Type /XObject Q 0 G 0 G 0.031 0.158 TD 45.663 0 0 45.147 426.844 513.418 cm 0000151303 00000 n Q q /FormType 1 q /F1 0.217 Tf Q /Length 55 /Meta424 Do 0.334 0.308 TD >> 0.531 0 l /FormType 1 354 0 obj << >> q 0 g stream q endstream 45.663 0 0 45.147 90.337 558.586 cm /FormType 1 0000186355 00000 n q ET >> 878 0 obj << /F3 21 0 R q q Q >> Q >> q 2.279 0.087 TD 0 w Q 45.663 0 0 45.147 426.844 107.652 cm 1.547 0.633 l /Pages 1 0 R /Matrix [1 0 0 1 0 0] /Length 102 /Length 51 0000250814 00000 n /Resources << /FormType 1 0000087130 00000 n >> 0000255859 00000 n >> BT 9.523 0.283 l /Meta697 712 0 R q endobj q endobj BT /Meta343 Do /F1 6 0 R Q >> 0.564 G endobj /BBox [0 0 1.547 0.33] Q /FormType 1 >> /FormType 1 0 w q Q stream 0 0.308 TD /BBox [0 0 1.547 0.314] >> Q 0 0.33 m >> q 11.988 0.283 l 0.458 0 0 RG /Font << [(1)] TJ /Meta336 Do 0 G 0 w 0 G q endstream 0 G q Q 2. 0.267 0.283 l /BBox [0 0 9.523 0.283] /Subtype /Form 0000253946 00000 n 0 g 0000164736 00000 n /Subtype /Form endstream 0 G 0.458 0 0 RG [(17)] TJ 414 0 obj << /FormType 1 /FormType 1 q 0.002 Tc q /BBox [0 0 1.547 0.283] /Meta285 298 0 R 45.527 0 0 45.147 523.957 687.317 cm q /Meta516 Do 0 G /Font << 0 0 l Q q q Q /Length 55 /Length 55 1 g Q >> /Meta198 209 0 R ET 895 0 obj << 0000148137 00000 n >> /Subtype /Form 0.458 0 0 RG /Resources << /Meta670 685 0 R q q /Font << q 1.547 0 l Q BT q q 0000043636 00000 n Q ET /Resources << endobj q /Meta720 735 0 R 0 g /Font << stream >> /Meta129 Do >> /F1 6 0 R >> 0000245043 00000 n /Resources << endstream 0.681 0.366 l >> 0.267 0 l 0 0 l 45.214 0 0 45.147 81.303 691.834 cm /F1 6 0 R ET q /Matrix [1 0 0 1 0 0] 0000343010 00000 n 0000016059 00000 n /Matrix [1 0 0 1 0 0] q /Meta347 360 0 R Q q q Q 923 0 obj << endobj q /Meta744 Do /Meta141 152 0 R /F1 0.217 Tf /BBox [0 0 1.547 0.633] /F1 6 0 R 0.267 0 l /Font << W* n /Subtype /Form 1.547 0.283 l /F1 6 0 R 0.458 0 0 RG 0 G /FormType 1 0 0.283 m >> Q 1 g >> endobj 0 0 l /Meta933 Do q 0 g /F1 6 0 R q /Meta310 323 0 R 1 g W* n q Q >> 45.324 0 0 45.147 54.202 573.643 cm >> ET 0.458 0 0 RG /Meta629 644 0 R 1072 0 obj << q 0 0 l >> /F1 0.217 Tf 0.165 0.366 l /Meta67 Do /Resources << 999 0 obj << /Type /XObject /F1 6 0 R 0 0 l 1 g endobj 0.015 w [(i)] TJ /Matrix [1 0 0 1 0 0] endstream /Meta390 Do 0.015 w /Meta130 Do /Length 55 Q /FormType 1 /Length 65 0.645 0.134 TD /FormType 1 stream /Matrix [1 0 0 1 0 0] endobj 866 0 obj << /Matrix [1 0 0 1 0 0] 0000213806 00000 n 683 0 obj << stream /FormType 1 BT /F1 0.217 Tf /Matrix [1 0 0 1 0 0] 0 0.633 m /Type /XObject 0 g /Type /XObject q 1013 0 obj << endobj endobj >> /BBox [0 0 9.523 0.633] 1.346 0.087 TD BT 0.267 0.5 l -0.001 Tc 0 g q stream >> /Matrix [1 0 0 1 0 0] -0.002 Tc /FormType 1 45.249 0 0 45.147 441.9 679.036 cm /F1 6 0 R endobj /Type /XObject q 1 J 1 g 1.547 0 l q q 1 g Q /F3 0.217 Tf Q 0 0 l /Matrix [1 0 0 1 0 0] Q /BBox [0 0 1.547 0.33] /Meta57 Do W* n /FormType 1 /Subtype /Form Q /Meta655 Do q /Meta1000 1015 0 R 0 G /F1 0.217 Tf 0 G q endobj stream 0000235338 00000 n /Font << 45.214 0 0 45.147 81.303 691.834 cm 0.564 G 0.381 0.087 TD q 45.663 0 0 45.147 314.675 679.036 cm endstream /BBox [0 0 1.547 0.283] 0 0.283 m >> Q /Meta407 Do 0 0.308 TD 0 0.283 m 0 0.087 TD endobj Q [(4)] TJ q /FormType 1 [(-)] TJ endobj q 0 0.283 m /Meta537 552 0 R 428 0 obj << q Q Q endobj Q 45.226 0 0 45.147 81.303 187.45 cm [(i)] TJ Q ET Q q /Font << Q Q -0.003 Tc endobj stream 559 0 obj << >> 774 0 obj << 1 g endobj >> 578.159 460.721 l 0 G 941 0 obj << /BBox [0 0 1.547 0.283] BT 828 0 obj << Q /Meta27 38 0 R /Meta391 404 0 R /BBox [0 0 9.787 0.283] /Matrix [1 0 0 1 0 0] endstream 0 g /BBox [0 0 1.547 0.283] stream 0000251892 00000 n 1047 0 obj << 1025 0 obj << endstream 0 g q q Q /FormType 1 /Type /XObject >> /Font << /Length 8 ET /FormType 1 /Type /XObject /Matrix [1 0 0 1 0 0] stream /Length 51 BT /Meta755 770 0 R >> 0000357348 00000 n Q [(-)] TJ /FormType 1 1.547 0.33 l endobj q q /Type /XObject 0 G q /FormType 1 q endobj /FormType 1 45.214 0 0 45.131 81.303 171.641 cm 0 g BT 0 G W* n /F1 0.217 Tf 325 0 obj << /Font << 45.527 0 0 45.147 523.957 181.427 cm /Meta63 74 0 R endstream q q /Meta888 903 0 R 45.663 0 0 45.147 202.506 368.125 cm 298 0 obj << 947 0 obj << q /Meta589 604 0 R BT Q 0 G /Subtype /Form /Meta440 455 0 R 9.791 0 0 0.283 0 0 cm endobj 1093 0 obj << /F1 6 0 R q q /Font << >> 0.314 0.283 l stream 0000042047 00000 n endobj /Resources << >> 0 g BT BT /BBox [0 0 9.523 0.283] /Meta224 Do 791 0 obj << /BBox [0 0 9.787 0.283] endstream 1.547 0 l 0000275349 00000 n 45.214 0 0 45.147 81.303 120.449 cm q Q Q 0 G q endstream 0 0.5 m ET BT 777 0 obj << /Meta986 Do /Length 67 /Resources << 1.547 0.633 l /Subtype /Form 9.791 0 0 0.283 0 0 cm q 0.564 G 0.334 0.473 TD 882 0 obj << [(D\))] TJ endstream Q Q /Font << 773 0 obj << q /Length 8 ET /Subtype /Form q W* n [( 3)] TJ /F1 0.217 Tf q >> q /F1 0.217 Tf 0 g 0.458 0 0 RG 593 0 obj << 45.249 0 0 45.131 217.562 143.034 cm q 45.249 0 0 45.147 105.393 720.441 cm q 0.267 0.283 l endobj stream 45.214 0 0 45.147 81.303 629.351 cm Q 0.458 0 0 RG 0 0 l q Q Q Q 1 g 1 g 0 w /Type /XObject stream /Meta1082 1099 0 R ET 0.047 0.087 TD /Resources << W* n /Matrix [1 0 0 1 0 0] /F1 6 0 R endobj 0000048646 00000 n /Matrix [1 0 0 1 0 0] ET 1028 0 obj << 0000364923 00000 n q q [(i)] TJ Q stream Q /FormType 1 1080 0 obj << 45.214 0 0 45.147 81.303 120.449 cm /Resources << 0.314 0.283 l 0 G stream 0.267 0.5 l endstream /Type /XObject /Subtype /Form >> 1 j 0.598 0.437 TD 0 G >> /Matrix [1 0 0 1 0 0] Q 583 0 obj << q >> q [(C\))] TJ 0000066252 00000 n >> [(i)] TJ /FormType 1 q >> /FormType 1 /Length 55 45.249 0 0 45.147 217.562 630.856 cm /F1 6 0 R stream /XObject << 1.114 0.087 TD stream q 0.015 w 45.663 0 0 45.147 202.506 718.183 cm [(65)] TJ 0 g endstream Q /Subtype /Form -0.007 Tc Q 445 0 obj << /FormType 1 0 w /Type /XObject Q Q /Length 55 q stream 0 G /Matrix [1 0 0 1 0 0] /Type /XObject Q 1017 0 obj << 0 G stream 0000173492 00000 n /Font << endstream q /F3 21 0 R /Meta531 546 0 R BT /Length 66 BT /FormType 1 BT q endstream 0.564 G 45.249 0 0 45.131 217.562 216.057 cm /Length 55 >> /BBox [0 0 1.547 0.283] q Q /Meta1049 1066 0 R q BT /Length 55 endstream Q Q endstream endobj >> /F1 0.217 Tf 0 g Q >> /Meta995 Do ET 0.564 G /Font << 1 g q /Subtype /Form /Length 63 /Meta593 Do /Type /XObject endstream /F1 6 0 R /Type /XObject /Length 51 1.547 0 l /Matrix [1 0 0 1 0 0] -0.007 Tc 0.267 0.087 TD 0 0 l 0 0.5 m 0 G /F1 0.217 Tf /BBox [0 0 1.547 0.283] 0 g q Q endstream Q 0 0 l stream Q /F1 0.217 Tf 0 0 l W* n 0.564 G /F1 0.217 Tf /Length 55 /F3 21 0 R Q >> [(i\)\()] TJ /Subtype /Form 0 g /Meta328 Do q /Meta685 Do /Type /XObject /Meta668 683 0 R /Resources << 0 0.087 TD 949 0 obj << Q 0000239256 00000 n Q /Font << 45.249 0 0 45.413 217.562 423.833 cm 0.267 0.283 l Q /BBox [0 0 9.523 0.283] 1.547 0.283 l q 45.663 0 0 45.147 314.675 558.586 cm endstream /Matrix [1 0 0 1 0 0] /Font << /Matrix [1 0 0 1 0 0] 0 0 l [(9)] TJ >> BT /Type /XObject >> q endstream /FormType 1 >> q stream /Meta798 Do q q /Type /XObject 0000153249 00000 n 0000283922 00000 n >> [(-)] TJ 0 w >> /F1 0.217 Tf 0 0.283 m endstream >> 0 G 0.001 Tc 0.015 w stream /Matrix [1 0 0 1 0 0] Q endstream endobj /FormType 1 ET q /F1 0.217 Tf 0 G /Subtype /Form /Matrix [1 0 0 1 0 0] Q /F3 21 0 R q /Type /XObject /Length 55 [(-)] TJ 0 0.283 m /Meta255 266 0 R >> /Meta526 541 0 R /Matrix [1 0 0 1 0 0] /Meta983 998 0 R /Length 66 /Meta768 Do /Length 68 endstream 45.249 0 0 45.527 441.9 558.586 cm Q /Type /XObject 0.334 0.308 TD 0.267 0.283 l Q q Q [(3)] TJ /F1 6 0 R >> /Subtype /Form /Meta644 659 0 R /Meta869 884 0 R 0.267 0.283 l 45.249 0 0 45.413 217.562 263.484 cm /BBox [0 0 0.263 0.283] Q q /Subtype /Form stream 0000002675 00000 n Q 0 0.33 m 0 0 l /Subtype /Form Q 0 G endobj endstream W* n /Type /XObject >> q 1 g 1 g q Q 0 G /BBox [0 0 1.547 0.633] endobj Q /Type /XObject endstream q ET /Matrix [1 0 0 1 0 0] 1 g 1 j /F1 6 0 R endobj 2. [( i)] TJ Q >> /Length 55 0 G 0 g q endobj 0 0.087 TD >> 0 w Q endobj >> Q BT 0000341336 00000 n Q q /Matrix [1 0 0 1 0 0] Q /Meta942 957 0 R 0 G /Meta111 Do /Font << 9.523 0 l /Subtype /Form endstream 0.267 0.283 l Q /Meta405 420 0 R [(4)] TJ >> /Font << Q endobj q 0000020695 00000 n /F1 0.217 Tf 480 0 obj << Q >> /Meta333 Do Q 9.523 0.283 l /FormType 1 372 0 obj << q 390 0 obj << /Matrix [1 0 0 1 0 0] 296 0 obj << 0.458 0 0 RG 45.214 0 0 45.147 81.303 161.854 cm 0 0 l /Meta993 Do 9.523 0.283 l /F1 0.217 Tf Q >> /Meta192 Do /Subtype /Form /Meta44 Do 0 g >> /BBox [0 0 1.547 0.283] /F1 6 0 R /F1 6 0 R Q q 0 G 0.267 0.5 l W* n /Matrix [1 0 0 1 0 0] endstream /F1 0.217 Tf /FormType 1 0.267 0.283 l 45.249 0 0 45.147 329.731 447.923 cm 45.663 0 0 45.147 90.337 149.056 cm /Resources << /Resources << /Font << Q 0 0 l 0.564 G Q EMBED Equation.3 45 27 9 + 36i -27 - 36i 5. /Meta482 Do /Type /XObject 0 G 45.663 0 0 45.147 426.844 263.484 cm 226 0 obj << 0 w 0000199504 00000 n 0 0 l Q Q 0000156244 00000 n >> Q Q 0 0.283 m 0 0 l /Font << Q 516 0 obj << q 0000259079 00000 n [(-)] TJ /Length 55 Q q endobj /Length 102 0.458 0 0 RG BT 0.458 0 0 RG q >> >> q 0.334 0.087 TD stream 0 g q endstream 0 g 0 0.5 m 1 J /Matrix [1 0 0 1 0 0] /Type /XObject Q 0 0.283 m /FormType 1 0 g /BBox [0 0 1.547 0.633] Q BT Q W* n /BBox [0 0 9.787 0.283] ET q endobj >> /F1 6 0 R Q /Resources << [(+)] TJ >> /Matrix [1 0 0 1 0 0] 0 0.087 TD stream 0 0.308 TD 45.663 0 0 45.147 314.675 513.418 cm /F1 0.217 Tf /Subtype /Form /FormType 1 680 0 obj << 0 w /Meta332 345 0 R Q /Matrix [1 0 0 1 0 0] 0 0.283 m /Meta76 87 0 R q 1 g /BBox [0 0 1.547 0.283] ET /BBox [0 0 9.523 0.283] ET q 0.267 0 l /Matrix [1 0 0 1 0 0] ET /F1 6 0 R 0 G [(i)] TJ Q 364972 Q /Length 136 stream /F1 0.217 Tf >> /F1 0.217 Tf /Meta692 707 0 R /Matrix [1 0 0 1 0 0] 0 g q BT 0.458 0 0 RG >> /Length 62 /Meta608 Do /Subtype /Form /F1 0.217 Tf [( 9i)] TJ 0 G 0 0 l /Font << 0.149 0.158 TD q 1.547 0 l Q stream /Meta698 Do 0.267 0.5 l 0.015 w /F1 0.217 Tf /Length 67 >> q q Q 0 g Q q -0.002 Tc 1 g q q /Length 54 0 w -0.007 Tc 0.015 w 0000150815 00000 n stream 0000078466 00000 n q /Type /XObject -0.002 Tc /BBox [0 0 1.547 0.33] Q 0.531 0 l /Meta1073 Do 0 G endstream Q 0.767 0.366 l 1 j 0.015 w q 0 G q >> q /Meta63 Do BT /Font << 0.015 w /BBox [0 0 1.547 0.633] >> /BBox [0 0 1.547 0.283] Q Q 0000080017 00000 n /FormType 1 stream 0000275957 00000 n /Meta583 Do /Meta614 Do Q /Matrix [1 0 0 1 0 0] [(9)] TJ endobj 0.948 0.087 TD 0000133619 00000 n /Type /XObject Q /FormType 1 ET >> >> 1 j BT 0.015 w /BBox [0 0 1.547 0.283] 1 g 45.324 0 0 45.147 54.202 227.349 cm 0.564 G 0 0 l /F1 0.217 Tf 45.663 0 0 45.147 202.506 679.036 cm 45.249 0 0 45.147 441.9 325.214 cm Q 0.015 w q 0000265805 00000 n Q Q 911 0 obj << W* n 0000200417 00000 n endstream q /Type /XObject /Resources << 0000245288 00000 n /Meta542 Do q 0 g W* n W* n Q 688 0 obj << 1 j /F1 0.217 Tf /F3 0.217 Tf 0.564 G /Subtype /Form /Meta104 Do 0 g 0000050431 00000 n 1 g /Type 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217.562 325.214 cm /Matrix [1 0 0 1 0 0] >> 45.249 0 0 45.527 329.731 491.586 cm q 617 0 obj << /F1 0.217 Tf /BBox [0 0 1.547 0.633] endstream /Meta257 268 0 R /FormType 1 endobj stream Q /Matrix [1 0 0 1 0 0] /F3 0.217 Tf 45.663 0 0 45.147 90.337 535.249 cm /BBox [0 0 1.547 0.633] /Length 106 q Q W* n /Length 8 0 G 0.047 0.087 TD /Resources << /Font << q q Q /Subtype /Form /Meta606 Do /Type /XObject stream /FormType 1 q Q >> 0 G q >> q 0 w q /Meta367 380 0 R /Resources << Q /BBox [0 0 0.263 0.283] /BBox [0 0 1.547 0.33] /Subtype /Form /Type /XObject q endstream 984 0 obj << 0.015 w 0 0 l /Subtype /Form /Type /XObject /Type /XObject Q 0 G [(i)] TJ /Meta442 457 0 R Q q Q /Resources << >> 0.515 0.087 TD /Matrix [1 0 0 1 0 0] /Subtype /Form [(+)] TJ /Subtype /Form endobj BT 0.334 0.087 TD ET q /F3 21 0 R 0.531 0.158 TD Their final destination – MATHEMATICS p 3 complex numbers are built on the concept of being able to define square. 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