The modulus of the square root of the conjugate of $-7+24 \sqrt{-1}$ is ....

Let $z_1$ and $z_2$ be two complex numbers such that $z_1 + z_2$ and $z_1 z_2$ are both real. Then:

If ${z_1}, {z_2}, {z_3}$ are complex numbers such that $|{z_1}| = |{z_2}| = |{z_3}| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1$,then $|{z_1} + {z_2} + {z_3}|$ is

If $m_1, m_2, m_3$ and $m_4$ respectively denote the moduli of the complex numbers $1+4i, 3+i, 1-i$ and $2-3i$,then the correct relation among the following is:

If complex numbers $(x - 2y) + i(3x - y)$ and $(2x - y) + i(x - y + 6)$ are conjugates of each other,then $|x + iy|$ is $(x, y \in \mathbb{R})$.

If $z = \frac{1}{1 - \cos \theta + i \sin \theta}$ and $\theta$ is acute,then the modulus and amplitude of $z$ respectively are: