How can you use trigonometric functions to simplify $12 e^{\frac{π}{2} i}$ $12 e^( ( pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2016-06-14T13:57:18

$12 e^{\frac{π}{2} i} = 12 i$ $12 e^{pi/2i} = 12 i$

Using Moivre`s relationship

$e^{i θ} = cos (θ) + i sin (θ)$ $e^{i theta} = cos(theta)+i sin(theta)$

$12 e^{\frac{π}{2} i} = 12 (cos (\frac{π}{2}) + i sin (\frac{π}{2})) = 12 i$ $12 e^{pi/2i} = 12(cos(pi/2)+i sin(pi/2)) = 12 i$

How can you use trigonometric functions to simplify 12eπ2i 12 e^( ( pi)/2 i ) into a non-exponential complex number?