Versionen från 15 november 2025 kl. 19.24

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Sammanfattning: Komplexa tal på polär form

\( \quad \)

Ex.: \( \quad\; z \, = \, 3 + 4 \, i \; \implies \; r \; = \; | z | \; = \; \sqrt{3^2 + 4^2} \; = \; 5 \)

\( \qquad\qquad\qquad\qquad\;\, \implies \; v \; = \; \tan^{-1} (4/3) \; = \; 53,13^\circ \)

\( \qquad\quad z \, = \, 5 \, (cos\,53,13^\circ + i \, sin\,53,13^\circ) \)

Omvänt: \( \quad\;\; a \, = \, 5 \, cos\,53,13^\circ \, = \, 3 \qquad\qquad b \, = \, 5 \, sin\,53,13^\circ \, = \, 4\)

@@ Rad 25: / Rad 25: @@
 === <span style="color:#931136"> <math> r \; = \; | z | \; = \; \sqrt{a^2 + b^2} \; = \; </math></span> <span style="color:blue">Absolutbelopp</span> ===
-=== <span style="color:#931136"> <math> \tan v \, = \, b/a \; \implies \; v \, = \, \tan^{-1} (b/a) </math></span> ===
+=== <span style="color:#931136"> <math> \tan v \, = \, b/a \; \implies \; v \, = \, \tan^{-1} (b/a) \; = \; </math></span> <span style="color:blue">Argument</span> ===
 === <span style="color:#931136"> Omvänt<span>:</span> <math> \quad a \, = \, r \, \cos v \qquad b \, = \, r \, \sin v </math></span> ===