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

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

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

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

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

Number of solutions of the equation z^(2)+|z|^(2)=0 , where z in C , is

Find argument of the complex numbers z = sqrt3 + i

If complex number z(zne2) satisfies the equation z^(2)=4z+|z|^(2)+(16)/(|z|^(3)) , then what is the value of |z|^(4) ?

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

Show that the area of the triagle on the argand plane formed by the complex numbers Z, iz and z+iz is (1)/(2)|z|^(2)," where "i=sqrt(-1).