# Complex numbers - set of points

• Sep 22nd 2012, 10:29 AM
Tala
Complex numbers - set of points

{z ∈ C | Im(z) = 2 Re(z) − 2}
• Sep 22nd 2012, 10:36 AM
Plato
Re: Complex numbers - set of points
Quote:

Originally Posted by Tala
{z ∈ C | Im(z) = 2 Re(z) − 2}

That is just the set $\{(x,y)|~y=2x-2\}$.
• Sep 22nd 2012, 11:49 AM
Tala
Re: Complex numbers - set of points
But how do I draw it in the complex plane?
• Sep 22nd 2012, 11:59 AM
Plato
Re: Complex numbers - set of points
Quote:

Originally Posted by Tala
But how do I draw it in the complex plane?

The same way you graph it in $R^2$.

$\text{Re}(z)$ is the $x\text{-axis}$ and $\text{Im}(z)$ is the $y\text{-axis}$.

It is a line.
• Sep 22nd 2012, 12:11 PM
Tala
Re: Complex numbers - set of points
But how do I plot this in Re(z)-2 ?
• Sep 22nd 2012, 12:19 PM
Plato
Re: Complex numbers - set of points
Quote:

Originally Posted by Tala
But how do I plot this in Re(z)-2 ?

Can you plot $y=2x-2~?$ If you can that is the same graph as $\text{Im}(z)=2\text{Re}(z)-2$