# Thread: Find z in complex equation ?

1. ## Find z in complex equation ?

Hallo there!
In this problem I need to find all z number $\displaystyle z \in C.$ in the following equation.

$\displaystyle \mid z-1\mid =5$

and

$\displaystyle \mid 4-z^2\mid =z$

2. Originally Posted by Kluringen
In this problem I need to find all z number $\displaystyle z \in C.$ in the following equation.
$\displaystyle \mid z-1\mid =5$ and

$\displaystyle \mid 4-z^2\mid =z$
The first one is simply a circle of radius 5 and center (1,0).

The second has one two real positive roots? WHY?

3. Originally Posted by Plato
The first one is simply a circle of radius 5 and center (1,0).

The second has one two real positive roots? WHY?
Ok, but I need to find the roots to this problem with help of pen and paper, no calculator or mathematica etc.

4. Originally Posted by Kluringen
Ok, but I need to find the roots to this problem with help of pen and paper, no calculator or mathematica etc.
Just solve $\displaystyle |4-x^2|=x$ for real $\displaystyle x$.