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

Find the number of complex numbers satisfying [itex] |z|=z+1+2i[/itex]

2. Relevant equations

3. The attempt at a solution

Let z=x+iy

|x+iy| = (x+1)+i(2+y)

Squaring and taking modulus

|[itex]\sqrt{x^{2}+y^{2}}|^{2} = |(x+1)+i(2+y)|^{2}[/itex]

[itex]x^{2}+y^{2} = (x+1)^{2}+(2+y)^{2}[/itex]

Rearranging and simplifying I get

2x+4y+5=0

Now what to do next? Also Is there any other way to solve this question?

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# Homework Help: Find no. of Complex Numbers

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