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

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

2. Relevant equations

3. The attempt at a solution

Distributed the i and then the 1/2's in each term which gave:

[tex] \sqrt{\frac{a} {2} + \frac{ \sqrt {a^2+b^2}}{2}}} -({-\frac{a} {2} + \frac {\sqrt {a^2+b^2}}{2}}) = a+ib [/tex].

Next I squared both sides to eliminate the roots, which gives:

[tex]\frac{a}{2}+\frac{\sqrt {a^2+b^2}}{2} - \frac {a^2}{4} - \frac {a^2+b^2}{4}+\frac {2a\sqrt{a^2+b^2}}{4}= a^2+2abi-b^2[/tex].

From that point it doesn't seem to work out. Was I going in the right direction?

Thanks for your help.

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# Homework Help: Complex numbers problem - lots of Algebra

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