I have some trouble with the initial condition of this equation: $f(z) = u(x+iy)+iv(x+iy)$ where $u(x+iy)=x^2-y^2+x$ and initial condition $f(i)=-1+i$.
Can someone please help me how to come to solution with initial condition ?
My solution is:
$x^2-y^2+x + i(2xy+y+C)$ where C is constant. I know I have to somehow replace the constant with the initial condition but I really don't know how to do it. Maybe it is simple but I don't have a clue...
Thank you for your answers.
I was trying a solution which was suggested on this:
$f(z) = x^2 - y^2 + xy + i(-(x^2/2) + y^2/2 +2xy + C), f(1+i)=-2i$
and I came to solution: $Ci=-2i \implies C = -2$ but it is marked as incorrect, it has to be $C=-1$ am I doing something wrong ? I substituted $x=1,y=i$...