Complex numbers - set of points

**Tala** · September 22nd 2012, 10:29 AM

Can someone please help me describe this set of points

{z ∈ C | Im(z) = 2 Re(z) − 2}

**Plato** · September 22nd 2012, 10:36 AM

Originally Posted by Tala

Can someone please help me describe this set of points
{z ∈ C | Im(z) = 2 Re(z) − 2}

That is just the set $\{(x,y)|~y=2x-2\}$ .

**Tala** · September 22nd 2012, 11:49 AM

But how do I draw it in the complex plane?

**Plato** · September 22nd 2012, 11:59 AM

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.

**Tala** · September 22nd 2012, 12:11 PM

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

**Plato** · September 22nd 2012, 12:19 PM

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

Thread: Complex numbers - set of points