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Rúmfræðileg skýring á tvinntölu z og samoka
í tvinntalnasléttunni.
Samoki í stærðfræði er tvinntala,
, sem vensluð er ákveðinni tvinntölu, z á þann hátt að þverhlutinn er neikvæður þverhluti hinnar tvinntölunnar, en raunhlutinn er sá sami.
Tvinntala:
![{\displaystyle z=a+ib\,}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9DothAatK4ajKPoqi4oAo3ytmNntvDzAsNoNzEotw3yjBCztGOzji4)
þar sem
og
eru rauntölur, en i er þvertala og samoki hennar:
![{\displaystyle {\overline {z}}=a-ib.\ }](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9Aa2o0zjC3o2aNyjlFzjvEngs1zjK3yjdDztK0nqwQaqdEotlBa2s1)
![{\displaystyle {\overline {(z+w)}}={\overline {z}}+{\overline {w}}\!\ }](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8Oa2zAnDzCzAi5aDG2oAnEzNaPotFAzNrDaAoOyqs4zqi4ntrBoAhA)
![{\displaystyle {\overline {(z-w)}}={\overline {z}}-{\overline {w}}\!\ }](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9DztJDytFEygs1yge1z2hFaqeNzNi5oNJBaAe5zjwOngdEajoOagnE)
![{\displaystyle {\overline {(zw)}}={\overline {z}}\;{\overline {w}}\!\ }](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8NyjvCzjs2zAw3aqaOzAa4yqo2nAo3zNvFatoPo2rEoNC4oDKQzDw1)
ef
er ekki núll
ef og aðeins ef
er rauntala
fyrir heiltölu ![{\displaystyle n}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9FzDmPytC1njs1zDm5nDdCyqo1nteNa2sNzAnEntBBote2ajiPoDzE)
![{\displaystyle \left|{\overline {z}}\right|=\left|z\right|}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO82nArEaNwOz2i3zDiQztBAnDi5ngi0aNGOzDw2aAzDzNo0aNo0ztBF)
![{\displaystyle {\left|z\right|}^{2}=z{\overline {z}}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9Czjs0nAw2nqhEoNeOzDK3zqvEyqhEaDs4ntFEaqi1o2sNngdEyjFB)
ef
er ekki núll.