Thread: Continuous Functions?

Prove that the function satisfies the Cauchy Riemann Equations at z = 0, but is not differentiable at z = 0.

f(z) = i, if y=x^2 and z not equal to 0 or 0, if y not equal to x^2 or z=0

I can prove that the CRE hold, but am having problems with the second part. Solutions tell me that I can observe that f is not continuous at z=0, but why is this so?

Thanks.

Originally Posted by cm7251

Prove that the function satisfies the Cauchy Riemann Equations at z = 0, but is not differentiable at z = 0.

f(z) = i, if y=x^2 and z not equal to 0 or 0, if y not equal to x^2 or z=0

I can prove that the CRE hold, but am having problems with the second part. Solutions tell me that I can observe that f is not continuous at z=0, but why is this so?

Thanks.

I'm sorry, but could you you possibly rephrase this. I am having trouble understanding what it means ?

Maybe another member will swoop in though.

Sorry.

The function is defined in two ways;
1) f(z) = 0, if z = 0 or x^2
2) f(z) = i, if and y = x^2