How can you use trigonometric functions to simplify # 3 e^( ( 3 pi)/8 i ) # into a non-exponential complex number?

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How can you use trigonometric functions to simplify # 3 e^( ( 3 pi)/8 i ) # into a non-exponential complex number?

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Answer 1 · 2016-02-19T15:06:56

we can use Euler's formula to solve the problem

Explanation:

Euler's formula #e^(ix)=cosx -isinx #
let #p=3e^(3pi/8i)#
#p^2=9e^(3pi/4i)#
#p^2=9e^(3pi/4i)=9(cos(3pi/4)+isin(3pi/4)#
#p=3sqrt(cos(3pi/4)+isin(3pi/4)#
#p=3sqrt(-1/sqrt(2)+i 1/sqrt(2))#

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How can you use trigonometric functions to simplify # 3 e^( ( 3 pi)/8 i ) # into a non-exponential complex number?

1 Answer

Explanation:

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