[Calira]

I'm not sure the best way to start this problem:

I have a model of a 2D flow given by the potential

and need to find the velocity components in the x and y directions.

I know that but when I differentiate w and then try and split into real and imaginary components, I get horribly long fractions which doesn't seem right.
I've also tried writing and then evaluating the partial derivatives of phi and psi to get the velocity components, but again that leads to some very messy algebra.

Am I missing a slick method, or do I have to try and force my way through the algebra?
Any pointers in the right direction are welcome.

[Coursework.info]

It's been a while since you posted and nobody's replied yet...maybe you should check out MarkedbyTeachers.com, TSR's sister site. It has the largest library of coursework and essays in the UK.

They've got over 168,000+ essays, projects, assignments, coursework etc.. all written by GCSE, A Level and Uni students. You get access either by publishing some of your own work, or paying £4.99 for a month's access. Both ways give you unlimited access to all of the essays.

All their documents are submitted to Turnitin anti-plagiarism software, so it can't be misused, and the site’s used by hundreds of thousands of UK teachers and students.

Hopefully you'll find it useful

[yusufu]

IIRC you want u= for a standard non-complex potential. I can't recall how it works for a complex potential.
Are you simply trying to find and then taking the real and imaginary parts as components for u?