Find the complex number 'z' satisfying Re`(z^(2))=0, |z|= sqrt3`

Let z_(1) and z_(2) be complex numbers satisfying |z_(1)|=|z_(2)|=2 and |z_(1)+z_(2)|=3 . Then |(1)/(z_(1))+(1)/(z_(2))|=

Let the complex number z satisfy the equation |z+4i|=3 . Then the greatest and least values of |z+3| are

The points representing the complex numbers z for which |z+4|^(2)-|z-4|^(2) = 8 lie on

If z_(1) and z_(2) are two complex numbers satisfying the equation |(z_(1) + iz_(2))/(z_(1)-iz_(2))|=1 , then (z_(1))/(z_(2)) is

Consider the complex number z=(5-sqrt3i)/(4+2sqrt3i)

If (sqrt(5)+sqrt(3)i)^(33)=2^(49)z , then modulus of the complex number z is equal to a)1 b) sqrt(2) c) 2sqrt(2) d)4

The modulus of the complex number z such that |z+3-i| = 1 and arg(z) = pi is equal to

If z is a complex number such that Re (z) = Im (z), then :

For any two complex numbers z_1 and z_2 prove that Re(z_1z_2) = Re(z_1)Re(z_2) - Im(z_1)Im(z_2)

Let i= sqrt-1 . If a sequence of complex numbers is defined by z_(1)=0, z_(n+1)= z_(n)^(2)+i for n ge 1 , then find the value of z_(111) .