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Question

If z=reiθ, then |eiz| is equal to
  1. ercosθ
  2. eθ
  3. ersinθ
  4. eisinθ


Solution

The correct option is C ersinθ
z=reiθ=r(cosθ+isinθ)
iz=ir(cosθ+isinθ)
iz=rsinθ+ircosθ
eiz=ersinθ+ircosθ
=ersinθericosθ
|eiz|=|ersinθ||ericosθ|
=ersinθ|eiα|, where α=rcosθ
=ersinθ[cos2α+sin2α]12
=ersinθ

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