Fr 0568 # 59

[rhnsrbh]

can anybody teach me as how to apply cauchy reimann equation through the following problem?

here s the equation

f(z)=(2x+3y)+ig(x,y)

if g(2,3)=1, what is g(7,3)?

[enork]

The Cauchy-Riemann equations specify that a holomorphic function satisfies $$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$$ and $$\frac{\partial u}{\partial y } = -\frac{ \partial v}{\partial x}$$, where u is the real part of the function f (in this case u = 2x+3y) and v is the imaginary part of f (in this case v = g(x,y)), and x is the real part of z and y is the imaginary part of z. In this case I assume we're supposed to know that f is holomorphic. Why don't you try applying those equations to the function in question.