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

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

Points z in the complex plane satisfying "Re"(z+1)^(2)=|z|^(2)+1 lie on

The greatest positive argument of complex number satisfying |z-4|=R e(z) is A. pi/3 B. (2pi)/3 C. pi/2 D. pi/4

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

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

The point z in the complex plane satisfying |z+2|-|z-2|= ±3 lies on

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

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

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

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