A calculus of the absurd

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

• • $$\rbrackets {\frac {z}{w}}^{*}$$

• • $$\rbrackets {z^{*}}^{*}$$

• • $$\abs {z} = \abs {z^{*}}$$

• • $$\abs {zw} = \abs {z} \abs {w}$$

• • $$\abs {\frac {z}{w}} = \frac {\abs {z}}{\abs {w}}$$

• • $$\abs {z + w} \leqq \abs {z} + \abs {w}$$