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

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Answer 1 · 2016-10-09T19:47:18

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

#e^(ix) = cos(x) + sin(x)i#

Multiply by any magnitude, A:

#Ae^(ix) = Acos(x) + Asin(x)i#

Answer 2 · 2016-10-09T19:52:00

#(-sqrt3+i)/2#

Using Euler's formula #e^(ix)=sinx+icosx#...

#3e^[(5pi)/3i]=sin((5pi)/3)+icos((5pi)/3)#

#color(white)(aaaa)=-sqrt3/2+i**1/2color(white)(aaa)# from the unit circle

#color(white)(aaaa)=(-sqrt3+i)/2#