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Question

If z=cosθ+isinθ, then

A
zn+1zn=2cosnθ
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B
zn+1zn=2ncosnθ
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C
zn1zn=2isinnθ
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D
zn1zn=(2i)nsinnθ
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Solution

The correct options are
A zn+1zn=2cosnθ
C zn1zn=2isinnθ
We have 1z=1cosθ+isinθ=cosθisinθ
zn=(cosθ+isinθ)n=cosnθ+isinnθ
and 1zn=(cosθisinθ)n=cosnθisinnθ
Hence zn+1zn=2cosnθ and zn1zn=2isinnθ

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