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

1 Answer
Mar 3, 2016

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

Explanation:

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