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

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

The complex number z which satisfies the condition |(i+z)/(i-z)| = 1 lies on

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

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

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

Variable complex number z satisfies the equation |z-1+2i|+|z+3-i|=10 . Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

The complex number z satisfies z+|z|=2+8i . find the value of |z|-8

The solution of the equation |z| -z = 1 + 2i is

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