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

if z=x+iy and sqrt(z) = u+iv

u=±(1/√2)*√(x+√(x^2+y^2 ))

v=±(1/√2)*√(-x+√(x^2+y^2 ))

How must the signs on these result be chosen?

2. The attempt at a solution

I wondered if it was something to do with ensuring √(z) was always positive, but then ruled this out as it is a complex function. I don't really know where to do with this one! Thanks for your help

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# Sign of u and v in a complex variable

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