How to understand $Re(z) + Im(z) = 2$ & $Re(z) - Im(z) = 0$, $z \in \mathbb{C}$

Question

So I got stuck on a question asking me to plot in $\mathbb{C}$ the following two expressions ($z \in \mathbb{C}$): $$Re(z) + Im(z) = 2$$ $$Re(z) - Im(z) = 0$$

Now this should be easy enough...

If we set $z = x +iy$ the first equation should be:
$Re(x + iy) + Im(x +iy) = 2$ Which would give me: $x + y = 2$ and the line $y = - x + 2$
Which is wrong...

The same thing with the second equation:
$Re(x+iy) - Im(x+iy) = 0$ would give me: $x - y = 0$ and the line $y=x$
Which is also wrong...

Something obvious is missing from my understanding of this...

This should be correct,but you're only looking for the intersection of those 2 lines — kingW3, Jan 15 '15 at 21:15
You are right, this is not wrong, I was not understanding the question properly. Thank you! I have been pulling my hair for a while on this question now :) — Lukas Arvidsson, Jan 15 '15 at 21:21

score 1 · Accepted Answer · answered Jan 15 '15 at 21:25

1

$z=x+iy$.

According to your equations, $z$ is a point of both the lines $y=-x+2$ and $y=x$ so it's the intersection of the both! That's a linear system of two equations with two unknown numbers, if the two lines aren't parallel or same then $z$ is a single point which is the case. Find $z$ by fiding $x$ and $y$!

answered Jan 15 '15 at 21:25

Scientifica

8,781

Thank you! This is indeed correct! – Lukas Arvidsson Jan 15 '15 at 21:27
You're welcome! – Scientifica Jan 15 '15 at 21:32

How to understand $Re(z) + Im(z) = 2$ & $Re(z) - Im(z) = 0$, $z \in \mathbb{C}$

1 Answers1