MR-116. példa

Hozza egyszerűbb alakra az alábbi kifejezést:

$\frac{30}{\sqrt{2}+\sqrt{3}i}$

$\frac{30}{\sqrt{2}+\sqrt{3}i}$

$=\frac{30}{\sqrt{2}{+}\sqrt{3}{i}}·\frac{\sqrt{2}-\sqrt{3}i}{\sqrt{2}{-}\sqrt{3}}$

$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{{\left(\sqrt{2}\right)}^{{2}}{-}{\left(\sqrt{3}i\right)}^{{2}}}$

$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{{2}{-}{3}{{i}}^{{2}}}$

$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{2-3\left(-1\right)}$

$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{2+3}$

$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{5}$

$=6\left(\sqrt{2}-\sqrt{3}i\right)$
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