Question

1. For the points shown on the complex plane shown, specify both rectangular and polar coordinates of the points. 15 14 - 13 + - - 1 I -1 - 12 - - 14 +-•D - 15+ 16 a. Point A b. Point B c. Point d. Point D irectangular coordinates putacionales

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Answer 1

. Concept uniy Rectangular form (2) Re{z} 21 y = Im{z} In coordinates polar z can be za rlo Here, 8= 5x² + y2 (same in all quadrants ) different for different coordinates. o is Im {z} Case a ) First qual uadrant fo Re{z} y os tant Case b) Second quadrant 180- tan' La 20 Case (c) Thind quadrant 180°t tout 1 2 3 fourth quadrent -tamil 12 h Caselal) . Solution > A=8 Lo 'A=6132 271.56° 6.32 24 j6 rectangular 2²+62 = tamil liel (finst quadrant) = 71.569 4+ j4 rectangular U42+42 S.66 turnt B = ;) B=5.66 Laro 450 tanti 4 CS Scanned

ji) C = C=8 Lo E=3.64 2-3389 iv) P 3-j2 - rectangular J 32+22 = 3.61 - tant Š - 1 2 3 l ( Forth quadrent) C= 3:61 (33.69° E-33.691 1-j 4 rectangular 2:23 D=8 Lo - tanul '11 =-75.94 z 7. 512+.4 2 D = 2.23 _-75-960 j=fa a) Remember (j) (j') j -1 k) 8 ( 3 b) -j c). -1 = . 2 +6+) > -1 e) j? 1°(3) * ; =jo xj = (32)"xj >(-1)ºx j + j d) * Tj (-1) j = +) 2G) - 4 e) j3 j2 (94); = -1 g) (6) 474) h) jt G = (1-7*(4724 = -1xj. j j2 xi = j = -1 j XJ ICS Scanned with CamScanner

2= Jiso²+2502 X tan 1/250 1) + j4 (Initial rector) Explanation 0 because Multiplication of į two times (j') One time multiplication of i j 4 x j -4 - -jq (final) + One time multiply by I 0 -4 time by One more multiplication by 1 ii) + - 3 + 3 Initial final v again multiply by j -3j So j² jz is is required j team Q 4 Rectangular z= 180+ 25o 18or En X=25on (first quadrant Polar & Lo z = 180 12= 308 z 54.2 CS Scanned with CamScanner

4/2on za R - 9/xc b) 2= 120 - 1 EA 85. 85 2 1262+11 <-tant ㅗ $5X120 85 ro 120 Z-54.68 s a) ZE 150 225° Conversion to of polar 2=8 Lo j e ) rectangular ocese + j sin e 150 (co25'+ j sim 25°) 135.95 +j 63.39 za J N b) z = 480 Lso Using z = sin soo با -3 Z 480 [cos (-80) + j Sin (-80 [ los so j 472.7 480 z = 83.35 CS Scanned with CamScanner