lean_workbook_plus_45835

The more general $\left|ab\right|=\left|a\right|\left|b\right|$ also holds (the statement $\left|z\right|^2=\left|z^2\right|$ follows by using $a=b=z$ ).\n\nTo see this, observe that $\left|ab\right|^2=\left(ab\right)\left(\overline{ab}\right)=\left(a\overline{a}\right)\left(b\overline{b}\right)=\left|a\right|^2\left|b\right|^2,$ so since magnitudes are nonnegative, $\left|ab\right|=\left|a\right|\left|b\right|$ .