How can you use trigonometric functions to simplify 8 e^( ( 2 pi)/3 i ) 8e2π3i into a non-exponential complex number?

1 Answer
Jim G.
May 26, 2016

8(cos((2pi)/3)+isin((2pi)/3))=-4+4sqrt3 i8(cos(2π3)+isin(2π3))=−4+4√3i

Explanation:

Using color(blue)"Euler's identity"Euler's identity

color(red)(|bar(ul(color(white)(a/a)color(black)(re^(thetai)=r(costheta+isintheta))color(white)(a/a)|)))

here r = 8 and theta=(2pi)/3

rArr8e^((2pi)/3i)=8(cos((2pi)/3)+isin((2pi)/3))

=8(-1/2+(sqrt3)/2 i)=-4+4sqrt3 i

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