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How can you use trigonometric functions to simplify # 6 e^( ( 3 pi)/8 i ) # into a non-exponential complex number?

1 Answer

Jan 2, 2016

By using Euler's formula.

#6*e^((3π)/8i)=2.2961+5.5433i#

Explanation:

Euler's formula states that:

#e^(ix)=cosx+isinx#

Therefore:

#6*e^((3π)/8i)=6*(cos((3π)/8)+i*sin((3π)/8))=#
#=6*(0.3827+0.9239i)=#
#=6*0.3827+6*0.9239i=2.2961+5.5433i#

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