Question

Find all vectors v in the plane such that ||v||=1 and ||v+i||=1

Answer 1

If \(v=(x,y)\), then \(|v|=\sqrt{x^2+y^2}\).
\(i=(0,1)\)
\(|v+i|=|v-(-i)|\)
\(v_1\) and \(v_2\) are the vectors you need.