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# Showing g(z) is constant in C watch

1. Given that a function is differentiable on , then given that I need to show is constant in .

I know that I need to use that on a given disc then and g differentiable for some constant on , although I'm pretty much stuck at this point...

I initially tried using Cauchy Riemann equations out of desperation but I don't get anything useful... can anyone help me get the ball rolling?
2. What level is this?
3. (Original post by Bananas01)
What level is this?
Uni, although I think it'll probably be something straightforward that I just haven't spotted (as is the usual case).
4. (Original post by wanderlust.xx)
Uni, although I think it'll probably be something straightforward that I just haven't spotted (as is the usual case).
Just wondering because I'm doing uni maths next year.
5. It comes out quite quickly using Cauchy-Riemann equations...
6. (Original post by SimonM)
It comes out quite quickly using Cauchy-Riemann equations...
So and g diff and .

Then what can I do? Or am I taking the wrong approach here?
7. du^3/dy = 3u^2 du/dy (all d's partial).
8. (Original post by DFranklin)
du^3/dy = 3u^2 du/dy (all d's partial).
dear god im being slow

So basically I get

Buuuuut as a final question, I don't understand what happens if ? Or does this just mean ?
9. Isn't in 9u^4+1? Although it doesn't really matter.

Moving on, from context, u is real, so u^4 >=0. (If u is complex valued, f doesn't have to be constant. e.g. just take u = z).
10. (Original post by DFranklin)
Isn't in 9u^4+1? Although it doesn't really matter.

Moving on, from context, u is real, so u^4 >=0. (If u is complex valued, f doesn't have to be constant. e.g. just take u = z).
yeah i missed writing out a 3 somewhere, it is in fact 9. I understand, cheers!

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