Geometry of complex numbers

Dear professor,

How has your Easter been?

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|.

Thank you for your time.

Hope you had a good holiday.

———————————————

Reply:

The Easter break went by quite quickly. I was mostly working at the Institut Des Hautes Etudes Scientifiques in France, but my family got to roam around Paris a bit and attended some Easter events at the Notre Dame Cathedral .

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|,

after which the answer should be easy.

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