# How do I begin sketching the following set of points on the complex plane

The set of points I'm interested in is Re$(\bar{z} - i)=2$

Honestly, I have no idea how to even begin. So what I hope is that I can get some general guidelines and steps on how to approach and solve such questions.

Any help or insights is deeply appreciated.

• In this case, it's helpful to note that $\bar z - i$ has the same real part as $z$. – Omnomnomnom Jan 12 '17 at 13:54

Let $z=x+iy$ with $x,y \in \mathbb R$. Then
$$\bar{z} - i=x-i(y+1)$$
hence $Re(\bar{z} - i)=x=Re(z)$. Thus, you are looking for points $z$ such that
$$Re(z)=2.$$
• Yes. The line has the equation $x=2$ – Fred Jan 12 '17 at 14:00