Question #339519

3. Let Z = i

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

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


1
Expert's answer
2022-05-11T12:47:30-0400

(i)


z=i=1(cos(π2)+isin(π2))z=i=1\big(\cos(\dfrac{\pi}{2})+i\sin(\dfrac{\pi}{2})\big)

(ii)


z4=(i)4=14(cos(4π2)+isin(4π2))=1z^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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