# Modulus (Complex Number)

Definition : The modulus of a complex number $a+bi$ is $(a+bi)(a-bi) = a^2+b^2$.

The modulus of a complex number is its magnitude thus the modulus can be denoted as $\lVert z \rVert = z \bar{z} = \mathrm{Re}(z)^2+ \mathrm{Im}(z)^2$. For example $\lVert 3+2i \rVert = (3+2i)(3-2i) = 9+4 = 13$.