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Question

If z=reiθ, then find the value of |eiz|


A
eiθ
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B
eisin θ
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C
ersin θ
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D
ercos θ
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Solution

The correct option is C ersin θ
z=reiθ=r(cos θ+isin θ)
iz=ir(cos θ+isin θ)
=r sin θ+ir cos θ
eiz=e(r sin θ+ir cos θ)
=ersin θeri cos θ
|eiz|=ersin θ|eiα|, where α=r cos θ
=ersin θ[cos2α+sin2α]12
=ersin θ

Mathematics

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