Question

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

Answer 1

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

Explanation:

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`