Answer to Question #337132 in Complex Analysis for Busi

Question #337132

Let Z = i



(i) Write Z in a polar form



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

1
Expert's answer
2022-05-06T05:45:05-0400

(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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