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If z = r*e^(i*theta) with r, theta real, what is the value of |e^(iz)|?

1. e^(-r*cos(theta))
2. e^(r*cos(theta))
3. e^(r*sin(theta))
4. e^(-r*sin(theta))

Correct answer: e^(-r*sin(theta))

Solution

With z = r*cos(theta) + i*r*sin(theta), iz has real part -r*sin(theta), so |e^(iz)| = e^(-r*sin(theta)).

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