What is the modulus of the complex number $(1+2i)(-2+i)$?

If $13 e^{i \tan ^{-1} \frac{5}{12}} = a + i b$,then the ordered pair $(a, b) =$

If $z$ is a complex number with $|z| \geq 5$,then the least value of $\left|z+\frac{2}{z}\right|$ is

If $z = \frac{1}{2} - 2i$ is such that $|z+1| = \alpha z + \beta(1+i)$,where $i = \sqrt{-1}$ and $\alpha, \beta \in \mathbb{R}$,then $\alpha + \beta$ is equal to

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 $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex numbers $-i, \frac{1}{3}(1+i)$ and $-1+i$,then their increasing order is