Solving Complex Potential Equation - Find Streamfunction, Potential

[dopey9]

Homework Statement

Iv been given the complex potential equation ..iv been trying to split it into real and imaginary parts so i can find the streamfunction and potential for it...however the ln is making it difficult

Homework Equations

The Attempt at a Solution

iv tried taking out a factor of two from 2i +4 and raising it to the ln part...so i get ln (x+iy)^2...i expanded that but i still got imaginary parts inside

so i was wondering if anyone knows any other ways to split the equation into imaginary parts and real parts

 

[Dick]

You'll want to express x+iy in the form r*exp(i*theta) and then think about evaluating the log.

 

[dopey9]

You'll want to express x+iy in the form r*exp(i*theta) and then think about evaluating the log.

Thanks that makes sense..i got it in my notes but just don't when to apply it

 

[dopey9]

streamline question

i was wondering if my u is right, as my problem deals with two dimensional inviscid steady potential flow and there are are various ways to find u = u(r,theta)er + v(r,theta)etheta

u= (-2/r)*er +(2/r)*etheta

and if so i was wondering how to sketch streamlines...using the previous question posted above i found that the speed of the particle was
u= (-2/r)*er +(2/r)*etheta