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How can you use trigonometric functions to simplify # 5 e^( ( 3 pi)/2 i ) # into a non-exponential complex number?

1 Answer

Dec 29, 2015

Apply Euler's formula to convert the function into a trigonometric form, and then evaluate to find

#5e^((3pi)/2i) = -5i#

Explanation:

Using Euler's formula: #e^(itheta) = cos(theta)+isin(theta)#

#5e^(i(3pi)/2) = 5(cos((3pi)/2) + isin((3pi)/2))#

#= 5(0 + i(-1))#

#= -5i#

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