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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.

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    In this case, it's helpful to note that $\bar z - i$ has the same real part as $z$. – 2017-01-12

1 Answers 1

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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

$$Re(z)=2.$$

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    essentially a vertical straight line ? – 2017-01-12
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    Yes. The line has the equation $x=2$ – 2017-01-12