How can you use trigonometric functions to simplify $12 e^( ( 2 pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-04-29T00:31:42

$-6+6 sqrt(3)i$

Using the identity $e^(i theta) = cos(theta) + i sin(theta)$
Replacing $(2pi)/3$ for $theta$

$e^(((2pi)/3)i)$ = $cos((2pi)/3) + i sin((2pi)/3)$

$12 e^(((2pi)/3)i)$ = $12(cos((2pi)/3) + i sin((2pi)/3))$

$= 12( -1/2 + i sqrt(3)/2)$

$= -6 + 6sqrt(3)i$

How can you use trigonometric functions to simplify 12 e^( ( 2 pi)/3 i ) 12 e^( ( 2 pi)/3 i ) into a non-exponential complex number?