Simple question: Use Euler's formula to rewrite an expression

DWill
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Homework Statement


Use Euler's formula to write the given expression in the form a + ib:

e^(2-(pi/2)i)


Homework Equations


Euler's formula: e^(it) = cos(t) + i*sin(t)


The Attempt at a Solution


I'm not sure how to get started on this one... am I supposed to get the expression into the e^(it) form somehow first?
 
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Use the laws of exponentials to split it into e^2*e^(-i*pi/2) first. Now use Euler's formula on the second factor. The first one you know well.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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