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**a**+

**b**in terms of

*i***a**and

**b**. I am trying to figure his answer out for my self but am struggling. Here goes:

[tex](x+yi)^2=a+bi[/tex]

[tex]x^2+2xyi-y^2=a+bi[/tex]

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

[tex]2xy=b[/tex]

I can't rearrange these two equations to get x and y in terms of a and b. Even if I use a computer program to solve them for me, I get really complicated answers. Not like the solution in the book. Am I doing it wrong? Here is the solution he gives:

I have checked it and it works quite cleverly.

[tex]\sqrt{\frac{1}{2}(a+\sqrt{a^2+b^2})}+i\sqrt{\frac{1}{2}(-a+\sqrt{a^2+b^2}}[/tex]