# How can you use trigonometric functions to simplify # 6 e^( ( pi)/8 i ) # into a non-exponential complex number?

##### 1 Answer

Mar 25, 2016

#= 3sqrt{2+sqrt2} + i(3sqrt{2-sqrt2})#

#### Explanation:

Euler showed that for a complex number

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

In this case

#r = 6# #theta = pi/8#

Therefore,

You can use half angle formulas to find

#= 3sqrt{2+sqrt2} + i(3sqrt{2-sqrt2})#