How can you use trigonometric functions to simplify $9 e^{\frac{3 π}{4} i}$ $9 e^( ( 3 pi)/4 i )$ into a non-exponential complex number?

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Answer 1 · 2016-04-01T11:55:57

$= 9 (- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2})$ $=9(-sqrt2/2+isqrt2/2)$

$e^{i x} = cos x + i sin x$ $e^(ix)=cosx+isinx$

$9 e^{\frac{3 π}{4} i} = 9 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))$ $9e^((3pi)/4i)= 9(cos((3pi)/4)+isin((3pi)/4))$

$= 9 (- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2})$ $=9(-sqrt2/2+isqrt2/2)$

How can you use trigonometric functions to simplify 9e3π4i 9 e^( ( 3 pi)/4 i ) into a non-exponential complex number?