Aus Online Mathematik Brückenkurs 2

One way to determine the magnitude is to calculate the product \displaystyle (3-4i)(3+2i) and then to take the magnitude of the result, but for products we have that

\displaystyle |zw| = |z|\cdot |w|

and we can take the magnitude of the factors \displaystyle 3-4i and \displaystyle 3+2i and then multiply the magnitudes together,

\displaystyle \begin{align} |(3-4i)(3+2i)| &= |3-4i|\cdot |3+2i|\\[5pt] &= \sqrt{3^2+(-4)^2}\cdot\sqrt{3^2+2^2}\\[5pt] &= \sqrt{9+16}\sqrt{9+4}\\[5pt] &= \sqrt{25}\sqrt{13}\\[5pt] &= 5\sqrt{13}\,\textrm{.} \end{align}