IGNOU MTE 4 2018 - Obtain the polar and exponential representations of z1 , z2 and z1z 2

Question

Obtain the polar and exponential representations of z1 , z₂ and z1z 2 , where zi = 1/2 - 2i and z2 = 3 + i

02 Feb 2018

Answer :

Word Count : 198

For $z_1 = \frac{1}{2} - 2i$ and $z_2 = 3 + i$, we convert them to polar and exponential forms. Step 1: Find the modulus and argument of $z_1$ $$ r_1 = |z_1| = \sqrt{\left(\frac{1}{2}\right)^2 + (-2)^2} = \sqrt{\frac{1}{4} + 4} = \sqrt{\frac{17}{4}} = \frac{\sqrt{17}}{2} $$ Argument: $$ \theta_1 = \tan^{-1}\left(\frac{-2}{1/2}\right) = \tan^{-1}(-4) $$ Since $z_1$ is

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