How can you use trigonometric functions to simplify $10 e^{\frac{5 π}{3} i}$ $10 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-01-08T14:56:16

$10 (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3}))$ $10( cos((5pi)/3) + isin( (5pi)/3))$

making use of the fact that

$e^{\frac{5 π}{3} i = cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})}$ $e^((5pi)/3i = cos((5pi)/3) + isin((5pi)/3 )$

$\Rightarrow 10 e^{\frac{5 π}{3}} i = 10 (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3}))$ $rArr 10e^((5pi)/3)i = 10( cos((5pi)/3) + isin((5pi)/3))$

How can you use trigonometric functions to simplify 10e5π3i 10 e^( ( 5 pi)/3 i ) into a non-exponential complex number?