Not right! Clearly there should be no imaginary numbers inside your real-valued functions. If , then . See if that helps!
Okay. A) This just doesn't work. That's a pretty huge problem.
B (probably the answer to the problem))
We know any function on a complex variable can be decomposed:
Where u(x,y) and v(x,y) are real-valued functions.
Now, let similarly.
Thus, .
so
Right? But then what happens to the i's inside the real-valued functions?