Let `alpha` and `beta` be two fixed non-zero complex numbers and 'z' a variable complex number. If the lines `alphabarz+baraz+1=0` and `betabarz+barbetaz-1=0` are mutually perpendicular, then

If z and w are two non-zero complex numbers such that z=-w.

A non-zero complex number z is uniquely determined if

If |(z-z_1)/(z-z_2)|=1 , where z_1 and z_2 are fixed complex numbers and z is a variable complex number, then z lies on a

Let alpha,beta be fixed complex numbers and z is a variable complex number such that |z-alpha|^(2)+|z-beta|^(2)=k. Find out the limits for ' k 'such that the locus of z is a circle.Find also the centre and radius of the circle

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that