If z=reiθ,then |eiz|=

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Question

If z=r

e^{i θ}

,then |

e^{i z}

|=

Options:

A . ersinθ

B . e−rsinθ

C . e−rcosθ

D . ercosθ

Answer: Option B
:
B
if z=r

e^{i θ}

=r(cos

θ

+ isin

θ

)

\Rightarrow

iz=ir(cos

θ

+ isin

θ

)=-rcos

θ

+ irsin

θ

or

e^{i z}

=

e^{- r c o s θ + i r s i n θ}

=

e^{- s i n θ} e^{r i c o s θ}

or |

e^{i z}

|=

| e^{- r s i n θ} | | e^{i r c o s θ} |

=

e^{- r s i n θ}

[c o s^{2} (r c o s θ) + s i n^{2} (r c o s θ)]^{2}

=

e^{- r s i n θ}

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