For Any Complex Number z, The Minimum Value Of  is 

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