Betrag einer Komplexen Zahl I.58

$$\left\vert z\right\vert=\sqrt{x^{2}+y^{2}}$$

• $\left\vert z\right\vert\geq0$
• $\left\vert z\right\vert^{2}=z\bar{z}$ (also $\frac{1}{z}=\frac{\bar{z}}{\left\vert z\right\vert^{2}}$)
• $\left\vert z\right\vert=\left\vert-z\right\vert=\left\vert\bar{z}\right\vert=\left\vert-\bar{z}\right\vert$
• $\left\vert z_{1}z_{2}\right\vert=\left\vert z_{1}\right\vert\left\vert z_{2}\right\vert$
• Dreiecksungleichung
  $\left\vert\left\vert z_{1}\right\vert-\left\vert z_{2}\right\vert\right\vert\l... ...{1}+z_{2}\right\vert\leq\left\vert z_{1}\right\vert+\left\vert z_{2}\right\vert$