If three complex numbers are in $A.P.$,then they lie on

The maximum distance from the origin of coordinates to the point $z$ satisfying the equation $\left| z + \frac{1}{z} \right| = a$ is

Length of the line segment joining the points $-1 - i$ and $2 + 3i$ is

Given $z$ is a complex number such that $|z| < 2$,then the maximum value of $|iz + 6 - 8i|$ is equal to-

If $|z_1|=1, |z_2|=2, |z_3|=3$ and $|9z_1z_2 + 4z_1z_3 + z_2z_3| = 12$,then the value of $|z_1 + z_2 + z_3|$ is equal to :-

If a complex number $z=x+iy$ represents a point $P(x, y)$ in the Argand plane and $z$ satisfies the condition that the imaginary part of $\frac{z-3}{z+3i}$ is zero,then the locus of the point $P$ is