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

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Answer 1 · 2015-12-24T20:31:59

By using the Moivre formula.

The Moivre formula tells us that $e^(itheta) = cos(theta) + isin(theta)$ . You apply it here !

$3e^(i(2pi)/3) = 3(cos((2pi)/3) + isin((2pi)/3)) = 3(-1/2 + sqrt(3)/2) = -3/2 +(3sqrt(3))/2$

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