If `z=((1+isqrt3)^2)/(4i(1-isqrt3))` is a complex number then |z| is

(1+isqrt(3))^(12)-(1-isqrt(3))^(12)=

Argument of (1-isqrt(3))/(1+isqrt(3))

If (z + 3)/( z - 5i) = ( 1 + 4i)/(2) find the complex number z.

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_(1),z_(2), and z_(3) are three complex numbers such that |z_(1)| = 1, " " |z_(2)| = 2, " " |z_(3)| = 3 and |z_(1) + z_(2) + z_(3) | = 1, show that |9z_(1)z_(2) + 4 z_(1)z_(3) + z_(2)z_(3)| = 6 .

If z_(1),z_(2)andz_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|z_(1)+z_(2)+z_(3)|=1 , find the value of |1/z_(1)+1/z_(2)+1/z_(3)| .

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.