How can you use trigonometric functions to simplify $19 e^( ( 3 pi)/4 i )$ into a non-exponential complex number?

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Answer 1 · 2017-10-29T13:35:30

$-(19root2 2) /2 + i(19root2 2)/2$

We need to consider how $re^(itheta) = rcostheta + irsintheta$

In this circumstance $theta$ = $(3pi)/4$

And $r =19$

Hence $19e^((3ipi)/4)$ = $19( cos((3pi)/4) + isin((3pi)/4))$

Hence via evaluating $cos((3pi)/4)$ and $sin((3pi)/4)$ we get;

$19(-(root2 2) /2 + i(root2 2)/2)$

Hence yeilding our answer or $-(19root2 2) /2 + i(19root2 2)/2$

How can you use trigonometric functions to simplify 19 e^( ( 3 pi)/4 i ) 19 e^( ( 3 pi)/4 i ) into a non-exponential complex number?