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December 10th, 2009, 03:51 PM   #1
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Finding complex numbers that solves equation

Hi all

I'm trying to find the solution for the following equation



where z is a complex number. The solution should be written in the from

I've accomplished this some of the way



or

Since the above can be written

or or or

But I can't figure out how to express these as


Can anyone tell me how to do the last part?
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December 10th, 2009, 04:37 PM   #2
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Re: Finding complex numbers that solves equation

Hi;

Maybe this substitution would have been better:

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December 11th, 2009, 03:55 PM   #3
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Re: Finding complex numbers that solves equation

General approach - use polar form

a + bi = r exp(iq), where r = ?(a^2 + b^2) and q=arctan(b/a), noting that q is multivalued.

Use this form as an intermediate for taking square root, making sure you take into account multiplicity of the angle. After you have gotten the final results in polar, convert back to rectangle using a=rcosq and b=rsinq.
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December 13th, 2009, 06:51 AM   #4
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Re: Finding complex numbers that solves equation

Thanks to both of you. Your ideas did help me understand the problem a little better, and made me look some more into my own textbooks.

I actually ended up using another way to solve (I'm not sure what to call this in english, but directy translated here) "binomial equations":










Using the above method to find gives me



Then

, , ,

Using the method again gives me

,

,


Which was actually the solution given in the course material.
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