How can you use trigonometric functions to simplify $3 e^( ( 11 pi)/6 i )$ into a non-exponential complex number?

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Answer 1 · 2016-09-18T03:20:07

$(3sqrt3)/2-3/2i$

Use Euler's formula $e^(ix)=cosx+isinx$

$3e^[frac{11pi}{6}i]=3(cos((11pi)/6)+isin((11pi)/6))$

$3e^[frac{11pi}{6}i]=3(sqrt3/2+i(-1/2))$

$3e^[frac{11pi}{6}i]=(3sqrt3)/2-3/2i$

How can you use trigonometric functions to simplify 3 e^( ( 11 pi)/6 i ) 3 e^( ( 11 pi)/6 i ) into a non-exponential complex number?