IF `agt=1`, find all complex numbers z satisfying the equation `z+a|z+1|+i=0`

Find a complex number z satisfying the equation z+sqrt(2)|z+1|+i=0.

Find a complex number z satisfying the equation z+sqrt(2)|z+1|+i=0.

Find a complex number z satisfying the equation z+sqrt(2)|z+1|+i=0.

For every real number age 0 , find all the complex numbers z that satisfy the equation 2|z|-4az+1+ ia =0

For every real number c ge 0, find all complex numbers z which satisfy the equation abs(z)^(2)-2iz+2c(1+i)=0 , where i=sqrt(-1) and passing through (-1,4).

If z is a complex number satisfying the relation |z+ 1|=z+2(1+i) , then z is

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is

If z is a complex number satisfying the equation z^6 +z^3 + 1 = 0 . If this equation has a root re^(itheta) with 90^@<0<180^@ then the value of theta is

Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)/(3), |(z-4)/(z-8)|=1

If z is a complex number satisfying the equation |z-(1+i)|^2=2 and omega=2/z , then the locus traced by 'omega' in the complex plane is