`z_(1) and z_(2)` are the roots of the equaiton `z^(2) -az + b=0` where `|z_(1)|=|z_(2)|=1` and a,b are nonzero complex numbers, then

If w=|z|^(2)+iz^(2), where z is a nonzero complex number then

If z_(1),z_(2) are roots of equation z^(2)-az+a^(2)=0 then |(z_(1))/(z_(2))|=

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

If z_(1),z_(2) are the non zero complex root of z^(2)-ax+b=0 such that |z_(1)|=|z_(2)|, where a,b arecomplex numbers.If A(z_(1)),B(z_(2)) and /_AOB=theta,'O' being the origin,then prove a^(2)=4b cos^(2)((theta)/(2))

If z_(1) and z_(2) are the roots of the equation az^(2)+bz+c=0,a,b,c in complex number and origin z_(1) and z_(2) form an equilateral triangle,then find the value of (b^(2))/(ac) .

Let z_(1) and z_(2) be the roots of z^(2)+az+b=0 If the origin,z_(1) and z_(2) from an equilateral triangle,then

If one root of the equation z^(2)-az+a-1=0 is (1+i), where a is a complex number then find the root.