# Thread: Complex Numbers

1. ## Complex Numbers

Describe the set of points in the complex plane that satisfy the given equation:

$\displaystyle |z-1|=1$

$\displaystyle |z|+|-1|=1\Rightarrow \sqrt{x^2+y^2}+1=1\Rightarrow \sqrt{x^2+y^2}=0$

$\displaystyle x^2+y^2=0$

The answer is supposed to be a circle centered at (1,0) with a radius of 1.

What am I doing wrong?

2. Originally Posted by dwsmith
Describe the set of points in the complex plane that satisfy the given equation: $\displaystyle |z-1|=1$

$\displaystyle |z|+|-1|=1$ THIS IS WRONG
What am I doing wrong?
$\displaystyle |z-1|=1$ means $\displaystyle (x-1)^2+y^2=1$.
That is the circle with center (1,0) & radius 1.

3. Originally Posted by dwsmith
Describe the set of points in the complex plane that satisfy the given equation:

$\displaystyle |z-1|=1$

$\displaystyle |z|+|-1|=1\Rightarrow \sqrt{x^2+y^2}+1=1\Rightarrow \sqrt{x^2+y^2}=0$

$\displaystyle x^2+y^2=0$

The answer is supposed to be a circle centered at (1,0) with a radius of 1.

What am I doing wrong?
$\displaystyle z=x+iy$

$\displaystyle z-1=x-1+iy$

$\displaystyle |z-1|=\sqrt{(x-1)^2+y^2}=1$

$\displaystyle (x-1)^2+y^2=1$