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

If $x+iy = \frac{a+ib}{a-ib}$,prove that $x^{2}+y^{2}=1$.

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

The argument and modulus of $\frac{1 + i}{1 - i}$ are respectively:

$(z + a)(\bar z + a)$,where $a$ is real,is equivalent 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: