Finding Intercepts & Modulus of z3=3e^(-ipie/4)

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For z3=3e^(-ipie/4) where does the function intercept the imaginary axis and what is the modulus?
 
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Ry122 said:
For z3=3e^(-ipie/4) where does the function intercept the imaginary axis and what is the modulus?


I don't understand how this is supposed to be a function. What is your independent variable..? z..? z3..? z^3..?
 
sorry just let z3=z
 
Recall Euler's formula for that one.
 
Still, z=3e^{-i\pi \frac{e}{4}} is not a function but some fixed constant 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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