Locate the region in the Argand plane determiend by `z^(2) + bar(z)^(2) + 2|z|^(2) lt (8i(bar(z)-z))`

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

If the complex numbers z _(1) , z _(2) and z _(3) denote the vertices of an isosceles triangle, right angled at z _(1), then (z _(1) - z _(2)) ^(2) + (z _(1) - z _(3)) ^(2) is equal to A)0 B) (z _(2) + z _(3)) ^(2) C)2 D)3

The points representing the complex numbers z for which |z+4|^(2)-|z-4|^(2) = 8 lie on

If (pi)/(3) and (pi)/(4) are argument of z_(1) and bar(z)_(2) then the value of arg (z_(1)z_(2)) is

If z=1+i , then the argument of z^(2)e^(z-i) is

If z ^(2) + z + 1 = 0, where z is a complex number, then the value of (z + (1)/(z)) ^(2) + (z ^(2) + (1)/( z ^(2))) ^(2) + (z ^(3) + (1)/(z ^(3))) ^(2) +...( z ^(6) + (1)/(z ^(6)) )^(2) is

If z= r (cos theta + i sin theta) , then the value of (z)/(bar(z)) + (bar(z))/(z) is

If z (2- 2 sqrt3i)^(2)= i(sqrt3+i)^(4) , then arg(z)=