# Thread: Complex numbers - set of points

1. ## Complex numbers - set of points

{z ∈ C | Im(z) = 2 Re(z) − 2}

2. ## Re: Complex numbers - set of points

Originally Posted by Tala
{z ∈ C | Im(z) = 2 Re(z) − 2}
That is just the set $\{(x,y)|~y=2x-2\}$.

3. ## Re: Complex numbers - set of points

But how do I draw it in the complex plane?

4. ## Re: Complex numbers - set of points

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.

5. ## Re: Complex numbers - set of points

But how do I plot this in Re(z)-2 ?

6. ## Re: Complex numbers - set of points

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 $\text{Im}(z)=2\text{Re}(z)-2$