How do you multiply $e^{\frac{π}{3} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 3 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{π}{3} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 3 i) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2016-05-03T01:10:11

By using the rule $e^{a} e^{b} = e^{a + b}$ $e^a e^b = e^{a+b}$ .

Explanation:

$e^{i \frac{π}{3}} e^{i \frac{π}{2}} = e^{i (\frac{π}{3} + \frac{π}{2})} = e^{i 5 \frac{π}{6}} = cos (5 \frac{π}{6}) + i sin (5 \frac{π}{6})$ $e^{i pi/3} e^{i pi/2} = e^{i (pi/3+pi/2)} = e^(i 5 pi/6) = cos(5 pi/6) + i sin(5 pi /6)$ (trigonometric form)

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How do you multiply $e^{\frac{π}{3} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 3 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{π}{3} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 3 i) * e^( pi/2 i )$ in trigonometric form?