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I've been given the task of find the real part for the following expression

[tex]\sqrt{x+iy}[/tex]

And I'm a bit stuck. I figure that I'll just say that that equation is equal to some other imaginary number a+bi where 'a' is the real part and 'b' is the imaginary part, and try to solve for a. But after squaring both sides i get stuck immediately...

[tex]x+iy = a^2 + 2abi - b^2[/tex]

And i don't know where to go. Perhaps I'm going the wrong way with this one, any help would be appreciated.

Edit: Ok, i've made some progress...

I know then that

[tex]x = a^2 - b^2[/tex]

and

[tex]iy = 2abi[/tex]

So i try to get rid of the b term in the real one, but the only substitution I can make results in a y term being introduced into the real part, which is just adding another imaginary number in there...

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# Homework Help: Real part of a complex number

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