(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\sqrt[n]{Z}[/tex] has exactly n distinct value for integer n.

What can you say about non-integer n's ?

2. Relevant equations

[tex]\sqrt[n]{Z}={|Z|}^{1/n}.(cos((\theta+2k\pi)/n)+isin((\theta+2k\pi)/n)[/tex]

3. The attempt at a solution

I used Euler's formula to see clearly what the roots are if n is integer.

As it is told i find [tex]\sqrt[n]{Z}[/tex] has n roots.

But what if n is non-integer?

I've been told that if n is non-integer there will be infinite solution.

How could it be?

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# Non-integer roots of complex numbers

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