Find the non-zero complex numbers `z` satisfying ` z =i z^2dot`

Modulus of nonzero complex number z satisfying barz +z=0 and |z|^2-4z i=z^2 is _________.

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

Find the complex number omega satisfying the equation z^3=8i and lying in the second quadrant on the complex plane.

The number of complex numbers z satisfying |z-3-i|=|z-9-i|a n d|z-3+3i|=3 are a. one b. two c. four d. none of these

Find the number of complex numbers which satisfies both the equations |z-1-i|=sqrt(2)a n d|z+1+i|=2.

Find number of values of complex numbers omega satisfying the system of equaltion z^(3)=-(bar(omega))^(7) and z^(5).omega^(11)=1

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex cos numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

Let z be a complex number satisfying |z+16|=4|z+1| . Then

Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then find the value of |z|dot

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 , find the minimum value of |z_1-z_2|