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Question


If $$z=re^{i\theta}$$ then $$|e^{iZ}|=$$


A
ercosθ
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B
ercosθ
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C
ersinθ
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D
ersinθ
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Solution

The correct option is D $$e^{-rsin\theta}$$

$$\left | e^{iz} \right |=\left | e^{ire^{i\theta }} \right |$$


$$=\left |e^{ir(cos\theta +isin\theta) }\right |$$


$$=\left |e^{ircos\theta} \times e^{-rsin\theta}\right |$$


$$=e^{-r sin\theta}$$

Since $$|e^{ircos\theta}|=1$$


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