(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

N/A

3. 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!

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# Homework Help: Complex variables(2)

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