If $z_1 = 2 + 5i$,$z_2 = -1 + 4i$,and $z_3 = i$,then $\left| \frac{z_1 - z_3}{z_3 - z_2} \right| = $

If $|z_1| = |z_2|$ and $\text{amp}(z_1) + \text{amp}(z_2) = 0$,then

The complex number $z$ satisfies the condition $\left| z - \frac{25}{z} \right| = 24$. The maximum distance from the origin of coordinates to the point $z$ is:

If $\alpha$ and $\beta$ are different complex numbers with $|\beta| = 1$,then $\left| \frac{\beta - \alpha}{1 - \overline{\alpha}\beta} \right|$ is equal to

If $\bar{z}$ is the conjugate of the complex number $z$,then which of the following relations is false?

The real value of $\theta$ for which the expression $\frac{1 + i \cos \theta}{1 - 2i \cos \theta}$ is a real number is $(n \in I)$: