## 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 if

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 for any two complex numbers and 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

after which the answer should be easy.

### Like this:

Like Loading...

*Related*