How can you use trigonometric functions to simplify $26 e^( ( 3 pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2016-01-03T15:23:38

$26e^((3pi)/2 i)=-26i$

Use Euler's formula:
$e^(i phi)=cos phi+i sin phi$
where $phi$ is a number, which can be interpreted as angle in radians.

In this question $phi=(3pi)/2$ :
$26e^((3pi)/2 i)=26cos((3pi)/2)+26i sin((3pi)/2)$

Now substract period $2pi$ from the arguements.
$26cos(-pi/2)+26i sin(-pi/2)$
$=26cos(pi/2)-26i sin(pi/2)=26*0-26i*1=-26i$

How can you use trigonometric functions to simplify 26 e^( ( 3 pi)/2 i ) 26 e^( ( 3 pi)/2 i ) into a non-exponential complex number?