Complex Analysis - Question on differentiability of a complex function

Let be such that f(z)=Re(z). How would you go about determining where f is differentiable?

Re: Complex Analysis - Question on differentiability of a complex function

Let z = x + iy, and f(z) = u + iv,

when you do that you will find what u and v are, then you can use the C-R equations and find if/where they hold

Re: Complex Analysis - Question on differentiability of a complex function

Another way: if then,

So, for the limit that defines depends on .

Re: Complex Analysis - Question on differentiability of a complex function