Complex numbers involving triangle ABC.

Question

Please help me solve this problem, I've tried sketching a triangle on axes of Real against Imaginary number. But don't know how to proceed. Should I treat $v$ and $u$ as vectors? Should I apply $AB= v - u$?

Answer 1

Here is the outline, but you will need to do the calculations yourself.

1. Indeed, you need to get $AB$ first as $u-v$
2. What's the slope of the line? Say $m$
3. The slope of BC is $-1/m$
4. Write the equation of a line going through $B$, with a slope $-1/m$
5. Choose a point $C$ on this line. Write the distance to $B$, $|C-B|$.
6. This last one is twice $|u-v|$

Answer 2

Yes, for sum, subtraction and modulus you can treat the complex numbers as vectors. by $AB$ I suppose it is intended the length of the segment, thus $|u-v|$.