Solving Complex Analysis Problems - Get Advice Here!

buzzmath
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Can anyone give me some advice on how to solve this problem?

in the reflection principle if f(x) is pure imaginary then the conjugate of f(z)=-f(z*) where z* is the complex conjugate of z.

Any advice on where to start?

thanks
 
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hint: if f is purely imaginary, then one can write f(z)=iy, for some real number, y.
 

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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