Answer to Question #337132 in Complex Analysis for Busi

Question

Let Z = i

(i) Write Z in a polar form

(ii) Use De Moivre’s Theorem to determine Z^4

Answer 1

(i)

$$z=i=1\big(\cos(\dfrac{\pi}{2})+i\sin(\dfrac{\pi}{2})\big)$$

(ii)

$$z^4=(i)^4=1^4\big(\cos(4\cdot\dfrac{\pi}{2})+i\sin(4\cdot\dfrac{\pi}{2})\big)=1$$