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uruz
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Homework Statement
[tex]\sqrt[n]{Z}[/tex] has exactly n distinct value for integer n.
What can you say about non-integer n's ?
Homework Equations
[tex]\sqrt[n]{Z}={|Z|}^{1/n}.(cos((\theta+2k\pi)/n)+isin((\theta+2k\pi)/n)[/tex]
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?