- #1

kingwinner

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## Homework Statement

Let z=x+iy. Describe the locus of points z satisfying |z-i|=Re(z).

## Homework Equations

N/A

## The Attempt at a Solution

|z-i|=Re(z)

=> sqrt[x

^{2}+(y-1)

^{2}] = x

=> x

^{2}+(y-1)

^{2}= x

^{2}

=> (y-1)

^{2}= 0

=> y=1

But the answer says y=1 and x≥0. Why? I think maybe I'm not getting the x≥0 because my implcations above isn't "if and only if". But what exactly is the reason and how can we rigorously justify that x≥0?

Any help is appreciated!