- #1
SALAAH_BEDDIAF
- 15
- 0
Let [tex]f(x+iy) = \frac{x-1-iy}{(x-1)^2+y^2}[/tex]
first of all it asks me to show that f satisfies the Cauchy-Riemann equation which I am able to do by seperating into real and imaginary [itex]u + iv : u(x,y),v(x,y)[/itex] and then partially differentiating wrt x and y and just show that [itex] \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} , \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} [/itex] and then it asks to express f in terms of z i.e f(z) =...
I have no idea where to begin with this
first of all it asks me to show that f satisfies the Cauchy-Riemann equation which I am able to do by seperating into real and imaginary [itex]u + iv : u(x,y),v(x,y)[/itex] and then partially differentiating wrt x and y and just show that [itex] \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} , \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} [/itex] and then it asks to express f in terms of z i.e f(z) =...
I have no idea where to begin with this