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Transpose of a Matrix

If z=reiθ t...

Question

If $z = r e^{i θ}$ then $| e^{i Z} | =$

A

e^{r cos θ}

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B

e^{- r cos θ}

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C

e^{r s i n θ}

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D

e^{- r s i n θ}

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Solution

The correct option is D $e^{- r s i n θ}$
$∣ ∣ e^{i z} ∣ ∣ = ∣ ∣ e^{i r e^{i θ}} ∣ ∣$

$= ∣ ∣ e^{i r (c o s θ + i s i n θ)} ∣ ∣$

$= ∣ ∣ e^{i r c o s θ} \times e^{- r s i n θ} ∣ ∣$

$= e^{- r s i n θ}$
Since $| e^{i r c o s θ} | = 1$

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