Sign of u and v in a complex variable

[Fixxxer125]

Homework Statement

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

 

[tiny-tim]

Hi Fixxxer125!

if z=x+iy and sqrt(z) = u+iv …

Do the obvious …

square the second equation: x + iy = z = (u + iv)²,

then equate real and imaginary parts (separately). ​

 

[Fixxxer125]

Ah brilliant, thanks!