How can you use trigonometric functions to simplify # 19 e^( ( 5 pi)/3 i ) # into a non-exponential complex number?

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How can you use trigonometric functions to simplify # 19 e^( ( 5 pi)/3 i ) # into a non-exponential complex number?

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Answer 1 · 2016-04-14T01:19:53

I found: #9.8-16.4i#

Explanation:

We can use Euler Form of the complex number and the conversion into trigonometric form to get to the normal #a+ib# form as:
#19e^((5/3pi)i)=19[color(red)(cos(5/3pi)+isin(5/3pi))]=#
evaluating our trig forms we get:
#=19[0.5-0.866i]=9.8-16.4i#

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How can you use trigonometric functions to simplify # 19 e^( ( 5 pi)/3 i ) # into a non-exponential complex number?

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