How do you multiply $e^{\frac{15 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 15 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{15 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 15 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2016-01-12T15:15:50

$e^{\frac{19 π i}{8}}$ $e^((19pii)/8)$

Explanation:

When multiplying two numbers that are raised to powers, you add the powers.
Therefore $e^{\frac{15 π i}{8}} \cdot e^{\frac{π i}{2}}$ $e^((15pii)/8)*e^((pii)/2)$
$= e^{(\frac{15}{8} + \frac{1}{2}) \cdot π i}$ $=e^((15/8+1/2)*pii)$
$= e^{\frac{19 π i}{8}}$ $=e^((19pii)/8)$

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How do you multiply $e^{\frac{15 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 15 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{15 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 15 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?