Finding streamfunction from complex potential F(z)=U(z²+4a²)^1/2

[Lucus]

I need to find the streamfunction of the complex potential
F(z)=U(z^2 + 4a^2)^1/2, where U and a are constants and z=x+iy. I can't figure out how to separate the real and imaginary parts in order to isolate the streamfunction from the velocity potential. Thanks in advance for any help!

 

[jaap de vries]

Just write the equation as

U*R^(1/2)*e^(i*theta/2)

Just write out z and you will find R and theta.

then use the identity k*e^(i*theta) = k*(cos(theta) + i*sin(theta))

that way you separate the potential = k*cos(theta)
and the streamfunction is k*sin(theta)

Sorry that I didn't use latex, it can get confusing
let me know if this helped you out or not
Jaap

 

[Lucus]

Thank you, Jaap de Vries, for responding to my question. Your answer is very helpful. Thanks again!