When we separate f(z) as , u and v are real valued functions. Notice that v is real valued and iv is imaginary.
So if the book gives , then there's no trick.
Hi I got a question, which I think may be a trick question.
"State Cauchy Riemann equations for real valued functions u(x,y), v(x,y).
we know a function is generally of the form
f(z) = u(x,y) + iv(x,y).
but U is the real part and V is the imaginary. so why does the question say "state the CRE for REAL VALUED FUNCTIONS u(x,y), v(x,y)."
Well, I should've been more precise.
v(x,y) is a real function. It's also the imaginary part of f(z).
For example, let z = 3 + 5i. The imaginary part of z is 5, which is a real number.
For example, let . We can write . So here and . Now you say, is 2xy a real or complex function? (x and y are real values).