(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that f(z) = zRez is differentiable only at z=0,

find f'(0)

3. The attempt at a solution

This should be easy. I find the limit as z_0 approaches 0 of [f(z+z_0) - f(z)]/(z_0) for this function...expand it out, simplify, and find what the limit is when z_0 is purely imaginary vs purely real. I did this, and I got x for the real part and x_0 + 2x + iy for the imaginary part. They're different, so it's not differentiable everywhere.

But apparently it's differentiable only at z=0. So I tried plugging in z=0 and resolving, and I got different values for z_0 real and imaginary.

I get, for the limit when z_0 is only real: 1

When z_0 only imaginary: x_0.

What's going on? Is there some other way to differentiate a complex function that's not using the limit?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex show differentiable only at z=0

**Physics Forums | Science Articles, Homework Help, Discussion**