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Question

Find the value of (cosθ+isinθ)n where θϵR,nϵI,i=1

A
n(cosθ+isinθ)
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B
ncosθ+isinnθ
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C
cosnθ+isinnθ
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D

cosnθ+insinθ

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Solution

The correct option is C cosnθ+isinnθ
Given (cosθ+isinθ)n (1)
We know eiθ=cosθ+isinθ
We can replace in equation (1)
From equation 1 we get, (eiθ)n
=einθ
This can be written as (cosnθ+isinnθ)

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