How can you use trigonometric functions to simplify $9 e^{\frac{7 π}{4} i}$ $9 e^( ( 7 pi)/4 i )$ into a non-exponential complex number?

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Answer 1 · 2018-06-11T10:48:31

$9 e^{\frac{7 π}{4} i} = 6.363961 - 6.363961 i$ $9 e^((7 pi)/4 i) =6.363961- 6.363961 i$

$9 e^{\frac{7 π}{4} i}$ $9 e^((7 pi)/4 i )$

We know $e^{i θ} = cos θ + i sin θ$ $e^(i theta) = cos theta +i sin theta$

$θ = \frac{7 π}{4} \approx 5.497787$ $theta= (7 pi)/4 ~~ 5.497787$

$:. 9 e^((7 pi)/4 i) = 9(cos ((7 pi)/4)+ i sin ((7 pi)/4))$ or

$9 e^((7 pi)/4 i) =6.363961- 6.363961 i$ [Ans]

How can you use trigonometric functions to simplify 9 e^( ( 7 pi)/4 i ) 9e7π4i 9 e^( ( 7 pi)/4 i ) into a non-exponential complex number?