Let z1,z2,z3 are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z1,z2,z3 are in the clockwise sense and z1 = 1+i√3, then:
=
|z1|=|z2|=|z3|=2
Z1Z2 = ∣∣Z1Z2∣∣e2πi/3
⇒Z2 = (1+i√3)e−2πi/3
⇒Z2 = (1+i√3)⎧⎪⎩−12−i√32⎫⎪⎭
⇒Z2 = 1−√3i
⇒Z3Z2 = ∣∣Z1Z2∣∣e2πi/3
⇒Z3 = (1−√3i)⎧⎪⎩−12+i√32⎫⎪⎭ = -2