How can you use trigonometric functions to simplify $21 e^( ( pi)/2 i )$ into a non-exponential complex number?

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Answer 1 · 2016-03-03T02:19:59

$21 e^{i (pi/2)} = 21 i$

There is this identity which is very useful.

$r e^{i theta} = r (cos theta + i sin theta)$

In this case,

$r = 21$

$theta = pi/2$

So plugging the values in

$21 e^{i pi/2} = 21 (cos (pi/2) + i sin (pi/2))$

$= 21 ((0) + i (1))$

$= 21 i$

How can you use trigonometric functions to simplify 21 e^( ( pi)/2 i ) 21 e^( ( pi)/2 i ) into a non-exponential complex number?