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Question

The polar form of (i25)3 is


A

cosπ2+i sin π2

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B

cos π+i sin π

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C

cos π+i sin π

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D

cos π2i sin π2

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Solution

The correct option is D

cos π2i sin π2


(i25)3=(i)75=(i)4×18+3=(i)3=i ( i4=1)Let z=0i

Since, the point (0, -1) lies on the negative direction of imaginary axis.

Therefore, arg (z) = π2

Modulus, r = |z| = |1| = 1

Polar form = r(cos θ+i sin θ)

=cos(π2)+i sin(π2)=cos π2i sin π2


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