If `|z|=2,` then find the locus of complex number `(a + bz),` where `a, b in R.`

Find the locus of complex number z, stisfying ( z + 1)^(n) = z^(n)

Find the locus of complex number z, stisfying ( z + 1)^(n) = z^(n)

Find the locus of a complex number z such that arg ((z-2)/(z+2))= (pi)/(3)

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.

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.

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.

Find the locus of a complex number z= x + yi , satisfying the relation |2z+ 3i| ge |2z + 5| . Illustrate the locus in the Argand plane.

Find the locus of a complex number z= x+ yi satisfying the relation arg (z-a)=(pi)/(4), a in R Illustrate the locus of z in the Argand plane

Find the locus of a complex number z=x +yi , satisfying the relation |z +i|=|z+ 2| . Illustrate the locus of z in the Argand plane

The locus of complex number z for which ((z-1)/(z+1))=k , where k is non-zero real, is