Answer to Question #339519 in Complex Analysis for Momo

Complex Analysis

Question #339519

3. Let Z = i

(i) Write Z in a polar form (2)

(ii) Use De Moivre’s Theorem to determine Z4

Expert's answer

(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"

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