Geometrical Representation of Conjugate of a Complex Number

Q. If $\frac{\pi }{2}<x<\frac{3\pi }{2}$, then write the value of $\sqrt{\frac{1+\cos 2x}{2}}$.

Q. If $\overline{z}=\overline{z_0}+A(z-z_0)$, where $A$ and $z_0$ are fixed complex numbers, then the locus of $z$ is a

1. parabola
2. hyperbola
3. circle
4. straight line

Q. find the normals at the ends of latus rectum (in first quadrant) of the ellipse 9x^2 +16y^2 =144

Q.

Conjugate of z is the mirror image of z along _______ on the Argand plane.

1. Imaginary axis

2. Origin

3. Real axis

4. None of these

Q.

If z = a + ib where a and b are less than zero. Conjugate of z lies on which quadrant in Argand plane.

1. I

2. II

3. III

4. IV