, show that z1, z2, z3 are the vertices of an equilateral triangle inscribed in a unit circle.
, the origin is the circumcentre of the triangle and circum-radius is 1. Hence by rotating in anti-clockwise direction about O,
Squaring and adding, 2 + 2 cos 2B = 1
Putting in (i), we get
Find all the values of the given root:
are the n, nth roots of unity,
If ω is fifth root of unity, then
, then find the equation whose roots are p and q.
Find the roots of the equation , whose real part is negative.
Let z1 and z2 be nth roots of unity which subtend a right angle at the origin. Then n must be of the form
For all complex numbers z1, z2 satisfying , the minimum value of
The complex numbers z1, z2 and z3 satisfying are the vertices of a triangle which is