Find the all complex numbers satisying the equation `2|z|^(2)+z^(2)-5+isqrt(3)=0, wherei=sqrt(-1).`

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).

The equation z^(2)-i|z-1|^(2)=0, where i=sqrt(-1), has.

Number of imaginergy complex numbers satisfying the equation, z^(2)=barz*2^(1-|z|) is s. 0 b. 1 c. 2 d. 3

If z_1, z_2 are two complex numbers satisfying the equation |(z_1 +z_2)/(z_1 -z_2)|=1 , then z_1/z_2 is a number which is :

If the points represented by complex numbers z_(1)=a+ib, z_(2)=c+id " and " z_(1)-z_(2) are collinear, where i=sqrt(-1) , then

The complex number z = x + iy , which satisfies the equation |(z-5i)/(z+5i)| =1 , lies on:

Represent the complex number z=1+sqrt3i in the polar form.

The complex numbers z_(1),z_(2),z_(3) stisfying (z_(2)-z_(3))=(1+i)(z_(1)-z_(3)).where i=sqrt(-1), are vertices of a triangle which is

If z is any complex number, prove that : |z|^2= |z^2| .

If z is any complex number satisfying abs(z-3-2i) le 2 , where i=sqrt(-1) , then the maximum value of abs(2z-6+5i) , is