# some algebra with complex numbers

• Apr 21st 2013, 04:24 PM
Ant
some algebra with complex numbers
Let $c,a \in \mathbb{C}$ be constants, let $n,m \in \mathbb{N}$, and let $z$ be a complex variable.

Is it true that:

$\bigl(c(|z|+1)^n +|a| \bigr) \ |z|^m = c_0 (|z|+1)^{n-m}$

For a suitable constant $c_0$?

It would be very helpful if this were true for a proof I'm trying to figure out...

Thanks
• Apr 24th 2013, 10:07 PM
hollywood
Re: some algebra with complex numbers
It doesn't seem like it would be possible - if $|z|$ is large, the left-hand side grows like $|z|^{n+m}$ and the right-hand side grows like $|z|^{n-m}$.

- Hollywood