---
title: Kompleksna števila – oblika in operacije
description: "Kompleksna števila: oblika a+bi, modul, konjugirano število in osnovne operacije."
url: https://astra-ai.co/sl/videos/kompleksna-stevila/
locale: sl
type: video-topic
keywords:
  - kompleksna števila
published: 2026-10-01T18:16:58.363Z
updated: 2026-10-01T18:16:58.363Z
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---

# Kompleksna števila

> Kompleksna števila razširijo realna števila z imaginarno enoto i, kjer je i² = -1. Omogočajo reševanje enačb, ki v realnih številih nimajo rešitve.

Kompleksna števila so razširitev realnih števil. Vsako kompleksno število zapišemo kot $z = a + bi$, kjer sta $a$ in $b$ realni, $i$ pa imaginarna enota z $i^2 = -1$.

## Oblika in osnovni pojmi

- **Realni del:** $a = \operatorname{Re}(z)$.
- **Imaginarne del:** $b = \operatorname{Im}(z)$.
- **Konjugirano število:** $\overline{z} = a - bi$.
- **Modul:** $|z| = \sqrt{a^2 + b^2}$.

## Operacije

- **Seštevanje:** $(a+bi)+(c+di) = (a+c)+(b+d)i$.
- **Množenje:** $(a+bi)(c+di) = (ac-bd)+(ad+bc)i$.
- **Deljenje:** množimo s konjugiranim imenovalcem.

## Geometrijski pomen

V kompleksni ravnini število $a+bi$ ustreza točki $(a,b)$. Argument (kot) in modul omogočata polarno obliko $z = r(\cos\varphi + i\sin\varphi)$.

## Zaključek

Kompleksna števila so nepogrešljiva v algebri, analizi, elektrotehniki in fiziki.