Question

Determine real and imaginary part of e ^ (5 + ipi / 2)​

Answer 1

Answer:

$real \: part \: = 0 \\ \\ imaginary \: part = {e}^{5} .$

Step-by-step explanation:

${e}^{(5 + i \frac{\pi}{2}) } = {e}^{5} . {e}^{i \frac{\pi}{2} } \\ \\ = {e}^{5} .( \cos( \frac{\pi}{2} ) + i \sin( \frac{\pi}{2} ) ) \\ \\ = {e}^{5} .i \\ \\ = i {e}^{5} \\ \\ real \: part \: = 0 \\ \\ imaginary \: part = {e}^{5} .$