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

Let $a \neq b$ be two non-zero real numbers. Then the number of elements in the set $X = \{ z \in \mathbb{C} : \operatorname{Re}(a z^2 + bz) = a \text{ and } \operatorname{Re}(b z^2 + az) = b \}$ is equal to

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

Let $z$ and $w$ be two non-zero complex numbers such that $|z| = |w|$ and $arg(z) + arg(w) = \pi$. Then $z$ is equal to:

If the complex numbers $z_1, z_2, z_3$ represent the vertices of an equilateral triangle such that $|z_1| = |z_2| = |z_3|$,then $z_1 + z_2 + z_3 = $

If the point $P$ represents the complex number $z=x+iy$ in the Argand plane and if $\frac{z+i}{z-1}$ is a purely imaginary number, then the locus of $P$ is: