Solve `z^(2)+ |z|=0`

Solve for z: z^(2)-(3-2i)z= (5i-5)

Solve 1/z + 1/(2+i) = 1/(1+3i)

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1)| + |z_(2)| , then arg ((z_(1))/(z_(2))) is equal to a)0 b) -pi c) -(pi)/(2) d) (pi)/(2)

The number of solutions of the equation z^(2)+bar(z)=0 , is

If z_(1) and z_(2) are complex numbers such that z_(1) ne z_(2) and |z_(1)|= |z_(2)| . If z_(1) has positive real part and z_(2) has negative imaginary part, then ((z_(1) +z_(2)))/((z_(1)-z_(2))) may be

If |z_(1)|= |z_(2)|= |z_(3)|=1 and z_(1) , z_(2), z_(3) are represented by the vertices of an equilateral triangle then which of the following is true?

Let z_(1) = 3 + 4i and z_(2) = - 1 + 2i . Then, |z_(1) + z_(2)|^(2) - 2(|z_(1)|^(2) + |z_(2)|^(2)) is equal to

Let x_1 and y_1 be real numbers. If z_1 and z_2 are complex numbers such that |z_1| = |z_2|=4 , then |x_1 z_1 - y_1 z_2|^(2) + |y_1 z_1 + x_1 z_2 |^(2) is equal to

If z+ sqrt2 |z+1| +ii=0 then the value of |z|^(2) is