Question

For any complex number z, the minimum value of  is 

Solution

Correct option is

2

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

SIMILAR QUESTIONS

Q1

Find the roots of the equation , whose real part is negative.

Q2

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin. Then n must be of the form

  

Q4
Q5

For all complex numbers z1z2 satisfying , the minimum value of 

Q6

, show that z1z2z3 are the vertices of an equilateral triangle inscribed in a unit circle. 

Q7

The complex numbers z1, z2 and z3 satisfying  are the vertices of a triangle which is

Q8

 

Find the complex numbers z which simultaneously satisfy the equation  

                     .

Q9
Q10

If z1z2z3 are complex numbers such that