Hi just a few questions on understanding the Cauchy-Riemann equations,
So for f(x+iy)=(x^2+y)+i(2xy-x)
I have my CR equations as:
du/dx=2x , dv/dx=2y-1
du/dy=1 , dv/dy=2x
=> 2x=2x and 2y-1= -1 , when y=0
As my first partials are continuous and exist, they satisfy the CR equations when y=0, does that mean the function is differentiable for z= x+i0? implying all real numbers?
Then does the derivative become
f'(z)= 2x -1i ?
There is no answer in the book for this, i just want to make sure i am doing it right
thanks for your help!!!