Definisjon

$$\mathbb{C} = \{ a+bi | a\in\mathbb{R},b\in\mathbb{R} \}$$

der \(i\) løyser likninga \(i^2=-1\).

$$ (1+2i) + (5-1i) = \mathrm{??} $$

$$ \begin{align} \begin{split} (1+2i) + (5-i) & = 1+2i + 5-i \\ & = 1+5 + 2i - i \\ & = 1+5 + (2-1)i \\ & = 6 + i \end{split} \end{align} $$

$$ (1+2i)\cdot (5-1i) = \mathrm{??} $$

$$ \begin{align} \begin{split} (1+2i) \cdot (5-i) &= 1\cdot5 + 2i\cdot 5 - 1\cdot i - 2i^2 \\ & = 5 + (10-1)i - 2(-1) \\ & = 5+2 - 9i \\ & = 7 - 9i \end{split} \end{align} $$