Thread: Using Cauchy Riemann show that these functions are nowhere differentiable

1. Using Cauchy Riemann show that these functions are nowhere differentiable

im stuck on these 2 problems on my homework for complex variables. the question is, using the cauchy riemann equations show that the following functions are nowhere differentiable. the two functions are f(z)=Re z and f(z)=|z|. Thank you!

2. Originally Posted by ChrisYee08
im stuck on these 2 problems on my homework for complex variables. the question is, using the cauchy riemann equations show that the following functions are nowhere differentiable. the two functions are f(z)=Re z and f(z)=|z|. Thank you!
Look at it this way:
$f(z)=\text{Re}(z)$ that means $u(x,y)=x~\&~v(x,y)=0$.

Carry on!

3. damn that was a quick reply haha. this is a nice site. what about for the modulus of z?

4. Originally Posted by ChrisYee08
damn that was a quick reply haha. this is a nice site. what about for the modulus of z?
Do something for yourself!
$|z|=\sqrt{x^2+y^2}$

5. yes i got that one actually b4 u relpied lol. ty tho

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use the cauchy riemann equations to show that the following functions are nowhere differentiable

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