Question
Prove that if $z=x+\mathrm{i} y$, then $\left|e^z\right|=e^x, \quad \operatorname{ph} e^z=y$.
Step 1
Step 1: Start by expressing the complex number \( z \) in terms of its real and imaginary components: \( z = x + \mathrm{i} y \), where \( x \) and \( y \) are real numbers, and \( \mathrm{i} \) is the imaginary unit. Show more…
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