Answer to Question #170360 in Complex Analysis for Sekyere Daniel

Question

.Whichofthefolowingistherectangularform ofofthecomplexnumber7.2e

a)0.509+i7.182 b)0.509-2.281c)2.182+i7.217 d)0.217+i7.7.182

Answer 1

a) $z=0.509+i7.182$

$|z|=\sqrt{(0.509)^2+(7.182)^2}\approx7.200$

$\theta=\tan^{-1}(\dfrac{7.182}{0.509})\approx1.500$

$$z=7.200e^{i1.500}$$

b) $z=0.509-i2.281$

$|z|=\sqrt{(0.509)^2+(-2.281)^2}\approx2.337$

$\theta=\tan^{-1}(\dfrac{-2.281}{0.509})\approx-1.351$

$$z=2.337e^{-i1.351}\ or\ z=2.337e^{i4.932}$$

c) $z=2.182+i7.217$

$|z|=\sqrt{(2.182)^2+(7.217)^2}\approx7.540$

$\theta=\tan^{-1}(\dfrac{7.217}{2.182})\approx1.277$

$$z=7.540e^{i1.277}$$

d) $z=0.217+i7.182$

$|z|=\sqrt{(0.217)^2+(7.182)^2}\approx7.185$

$\theta=\tan^{-1}(\dfrac{7.182}{0.217})\approx1.541$

$$z=7.185e^{i0.1541}$$

Answer

a) $z=0.509+i7.182=7.200e^{i1.500}$