How do you multiply $e^(( 4 pi )/ 3 i) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2018-07-12T21:41:57

$\frac{\sqrt3-i}{2}$

$e^{{4\pi}/3i}\cdot e^{\pi/2i}$

$=e^{{4\pi}/3i+\pi/2i}$

$=e^{i({4\pi}/3+\pi/2)}$

$=e^{{11\pi}/6i}$

$=\cos({11\pi}/6)+i\sin({11\pi}/6)$

$=\cos(2\pi-{\pi}/6)+i\sin(2\pi-{\pi}/6)$

$=\cos({\pi}/6)-i\sin({\pi}/6)$

$=\sqrt3/2-i 1/2$

$=\frac{\sqrt3-i}{2}$

How do you multiply e^(( 4 pi )/ 3 i) * e^( pi/2 i ) e^(( 4 pi )/ 3 i) * e^( pi/2 i ) in trigonometric form?