Bevisa att likheten gäller

$$\begin{gathered} \overline{\mathbf{z}\mathbf{-}\mathbf{w}}\mathbf{=}\overline{\mathbf{z}}\mathbf{-}\overline{\mathbf{w}} \\ \mathit{z}\mathbf{=}\mathit{a}\mathbf{+}\mathit{b}\mathit{i}\mathbf{\Rightarrow }\overline{\mathbf{z}}\mathbf{=}\mathit{a}\mathbf{-}\mathit{b}\mathit{i} \\ \mathit{w}\mathbf{=}\mathit{c}\mathbf{+}\mathit{d}\mathit{i}\mathbf{ }\mathbf{\Rightarrow }\overline{\mathbf{w}}\mathbf{=}\mathit{c}\mathbf{-}\mathit{d}\mathit{i} \\ \overline{\mathbf{z}}\mathbf{-}\overline{\mathbf{w}}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{-}\mathit{b}\mathit{i}\mathbf{)}\mathbf{-}\mathbf{(}\mathit{c}\mathbf{-}\mathit{d}\mathit{i}\mathbf{)}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathit{e}\mathit{l}\mathit{l}\mathit{e}\mathit{r}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathit{a}\mathbf{-}\mathit{c}\mathbf{)}\mathbf{-}\mathbf{(}\mathit{b}\mathbf{+}\mathit{d}\mathbf{)}\mathit{i} \\ \mathit{z}\mathbf{-}\mathit{w}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{+}\mathit{b}\mathit{i}\mathbf{)}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{(}\mathit{c}\mathbf{+}\mathit{d}\mathit{i}\mathbf{)}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathit{e}\mathit{l}\mathit{l}\mathit{e}\mathit{r}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathit{a}\mathbf{-}\mathit{c}\mathbf{)}\mathbf{+}\mathbf{(}\mathit{b}\mathbf{-}\mathit{d}\mathbf{)}\mathit{i} \end{gathered}$$ 

(a-c) = a och (b-d)i =bi om man ska skriva på z = a + bi formeln ellerhur? för att a-c är reella tal och bi-di är imaginära

$$\begin{gathered} \mathit{A}\mathit{l}\mathit{l}\mathit{t}\mathit{s}\mathit{å}\mathbf{,}\mathbf{ }\overline{\mathbf{z}\mathbf{-}\mathbf{w}}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{-}\mathit{c}\mathbf{)}\mathbf{-}\mathbf{(}\mathit{b}\mathbf{-}\mathit{d}\mathbf{)}\mathit{i} \\ \mathit{M}\mathit{e}\mathit{n}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\overline{\mathbf{z}}\mathbf{-}\overline{\mathbf{w}}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{-}\mathit{c}\mathbf{)}\mathbf{-}\mathbf{(}\mathit{b}\mathbf{+}\mathit{d}\mathbf{)}\mathit{i}\mathbf{ }\mathbf{ }\mathit{D}\mathit{e}\mathit{t}\mathbf{ }\mathit{s}\mathit{t}\mathit{ä}\mathit{m}\mathit{m}\mathit{e}\mathit{r}\mathbf{ }\mathit{j}\mathit{u}\mathbf{ }\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathbf{ }\mathit{a}\mathit{t}\mathit{t} \\ \overline{\mathbf{z}}\mathbf{-}\overline{\mathbf{w}}\mathbf{=}\overline{\mathbf{z}\mathbf{-}\mathbf{w}} \end{gathered}$$