## Geometry of complex numbers

Dear professor,

I was doing some revision and I came across a question I would like to ask you. Please enlighten me on it.

Find the least value of $|z|$ if $|z - i| = |z - 2|.$

Hope you had a good holiday.

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Regarding your question, note that $|z-w|$ for any two complex numbers $z$ and $w$ is just the distance between them regarded as points in the plane. In particular, you should be able to draw the line (why?) defined by the condition
$|z - i| = |z - 2|,$