# Complex exponential

## Homework Statement

write e^z in the form a +bi
z = 4e^(i*pi/3)

---------------------------------------
My guess:

z = 4*(cos(pi/3) + i*sin(pi/3))

e^z = e^(4*(cos(pi/3) + i*sin(pi/3))) = e^(4*cos(pi/3))*(cos(4*sin(pi/3)) + i*sin(4*sin(pi/3)))

but the solution says

e^(2)*(cos(2*sqrt(3)) + i*sin(2*sqrt(3)))

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gabbagabbahey
Homework Helper
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## Homework Statement

write e^z in the form a +bi
z = 4e^(i*pi/3)

---------------------------------------
My guess:

z = 4*(cos(pi/3) + i*sin(pi/3))

e^z = e^(4*(cos(pi/3) + i*sin(pi/3))) = e^(4*cos(pi/3))*(cos(4*sin(pi/3)) + i*sin(4*sin(pi/3)))

but the solution says

e^(2)*(cos(2*sqrt(3)) + i*sin(2*sqrt(3)))
Well, $\sin(\pi/3)=\frac{\sqrt{3}}{2}$, and I'm sure you know what $\cos(\pi/3)$ is...

Thanks for the help.
--------------------------------------
z = 4e^(i*pi/3)
z = 4*(cos(pi/3) + i*sin(pi/3))
z = 2 + 2*sqrt(3)
e^z = e^(2)*(cos(2*sqrt(3)) + i*sin(2*sqrt(3))