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**terrorsquid** Find and graph all $\displaystyle z \in \mathbb{C}$ that satisfy the equation $\displaystyle |z-2i|=|z+1|$.

So, I am finding the values where the distance from z to 2i is the same as the distance from z to -1 right?

My solution:

$\displaystyle |(x+yi)-2i|=|(x+yi)+1|$

$\displaystyle \sqrt{x^2+(y-2)^2}=\sqrt{(x+1)^2+y^2}$

$\displaystyle x^2+(y-2)^2}=(x+1)^2+y^2$

$\displaystyle x^2+y^2-4y+4=x^2+y^2+2x+1$

$\displaystyle y=-\frac{1}{2}x+\frac{3}{4}$

Is there anything more to it than that; now that I have the line?

Thanks.