The locus of point `z` satisfying `R e(1/z)=k ,w h e r ek` is a nonzero real number, is a. a straight line b. a circle c. an ellipse d. a hyperbola

The locus of the point (sqrt(3h),(sqrt(3)k+2)) if it lies on the line x-y-1=0 is straight line (b) a circle a parabola (d) none of these

Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

The number of terms in the expansion of (a+b+c)^n ,w h e r en in Ndot

If z=z_0+A( bar z -( bar z _0)), w h e r eA is a constant, then prove that locus of z is a straight line.

If |z|=1, then the point representing the complex number -1+3z will lie on a. a circle b. a parabola c. a straight line d. a hyperbola

If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight line c. a pair of straight line d. none of these

The locus of a point whose chord of contact with respect to the circle x^2+y^2=4 is a tangent to the hyperbola x y=1 is a/an ellipse (b) circle hyperbola (d) parabola

Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary part of z^2a n dz^3 are equal, then b/3 is ______.

If t and c are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t+b)/(t-c), z=x+i ydot Locus of z is (where a, b are complex numbers) a. line segment b. straight line c. circle d. none of these

If one root of the equation z^2-a z+a-1=0i s(1+i),w h e r ea is a complex number then find the root.