Exponential function of a complex number question?

[Mandynash]

Homework Statement

The question is located here http://i51.tinypic.com/nex2q1.jpg

Homework Equations

The value I have been given for a) is 5
The value I have been given for b) is 5PI/6

The Attempt at a Solution

Note that e^(a + bi) = e^a e^(bi) = e^a (cos b + i sin b).
(e^a is the modulus, and b is the argument, because |e^(bi)| = sqrt(cos^2(b) + sin^2(b)) = 1.)

Letting a = 5 and b = 5π/6 yields
e^(a+bi) = e^5 (cos 5π/6 + i sin 5π/6) = e^5 (-sqrt(3)/2 + i/2).

No idea what else I need to do! thanks in advance for helping

 

[micromass]

Looks good!