A calculus of the absurd

15.1.4 Properties of the complex conjugate and absolute value
  • • \((zw)^{*} = z^{*} w^{*}\)

  • • \(\rbrackets {\frac {z}{w}}^{*}\)

  • • \(\rbrackets {z^{*}}^{*}\)

  • • \(\abs {z} = \abs {z^{*}}\)

  • • \(\abs {zw} = \abs {z} \abs {w}\)

  • • \(\abs {\frac {z}{w}} = \frac {\abs {z}}{\abs {w}}\)

  • • \(\abs {z + w} \leqq \abs {z} + \abs {w}\)