For all complex numbers z1, z2 satisfying , the minimum value of
The two circles are and it passes through origin, the centre of C1
Hence circle C2 lies inside circle C1
Therefore minimum distance between them is
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
, show that z1, z2, z3 are the vertices of an equilateral triangle inscribed in a unit circle.