Solve Complex Potential: Streamfunction from Velocity Potential

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To find the streamfunction from the complex potential F(z)=U(z^2 + 4a^2)^(1/2), separate the real and imaginary parts by expressing it as U*R^(1/2)*e^(i*theta/2). Define z as x + iy to derive R and theta. Utilize the identity k*e^(i*theta) = k*(cos(theta) + i*sin(theta) ) to isolate the velocity potential as k*cos(theta) and the streamfunction as k*sin(theta). The discussion highlights the importance of correctly separating these components for clarity in fluid dynamics analysis. The provided method effectively aids in achieving the desired separation.
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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!
 
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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
 
Thank you, Jaap de Vries, for responding to my question. Your answer is very helpful. Thanks again!
 
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