For any complex number z, the minimum value of is
We have, for z ∈ C
Thus, minimum value of is 2 it is attained for any z lying on the segment joining = 0 and z = 2i.
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
, show that z1, z2, z3 are the vertices of an equilateral triangle inscribed in a unit circle.
The complex numbers z1, z2 and z3 satisfying are the vertices of a triangle which is
Find the complex numbers z which simultaneously satisfy the equation
If z1, z2, z3 are complex numbers such that