can someone explain how to do this problem. This is for complex numbers & exponential.

Question

write given problem in form a+bi
e^((5e)^(i*pi/3))

Answer 1

Start with e^iθ = cosθ + isinθ
using De Moivre's Theorem, and the fact that 5e = e^ln(5e)
(5e)^(i*pi/3) = cos(π ln(5e)/3) + i sin(π ln(5e)/3) = -0.9175 + 0.3977i
Now take
e^-0.9175 + 0.3977i
= e^-0.9175 (cos 0.3977 + i sin 0.3977)
= 0.3683 + 0.1547i

You can express it exactly, but it won't fit in the margins of this post.

Answer 2

its saying that this answer is wrong, i tried to redo it with ur steps, and use exact values. It saying it's wrong.