Prove that locus of z is a circle and find its centre and radius if `(z-i)/(z-1)` is purely imaginary.

If the ratio (1-z)/(1+z) is pyrely imaginary, then

Show that |(z -2)/(z - 3)| = 2 represents a circle, find its centre and radius.

Show that |(z -2)/(z - 3)| = 2 represents a circle, find its centre and radius.

The complex number z is purely imaginary , if

Find the locus of point z if z , i ,and iz , are collinear.

If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z lies on the circle whose centre is the point (1)/(2) (1+i) and radius is (1)/(sqrt2)

Variable complex number z satisfies the equation |z-1+2i|+|z+3-i|=10 . Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+ 1/z is

If |(z-2)//(z-3)|=2 represents a circle, then find its radius.

If z_1=10+6i and z_2=4+2i be two complex numbers and z be a complex number such that a r g((z-z_1)/(z-z_2))=pi/4 , then locus of z is an arc of a circle whose (a) centre is 5+7i (b) centre is 7+5i (c) radius is sqrt(26) (d) radius is sqrt(13)