News Categories Users + Create topic Tools Formulynas Matematikos formulių, taisyklių ir pamokų rinkinys Matavimo vienetai Matavimo vienetų sąryšiai ir jų konvertavimas Testai Interaktyvūs realiu laiku sprendžiami matematikos testai Egzaminai Ankstesnių metų matematikos PUPP ir VBE užduotys su sprendimais Log in
       

Complex numbers basic formulas

Advanced math

Algebraic form of complex number, where [tex]i^2=-1[/tex]. $${z=x+iy}$$
Trigonometric form of complex number, where [tex]r=\sqrt{x^2+y^2}[/tex], [tex]{\cos(\varphi)=\frac{x}{r}}[/tex] and [tex]\sin(\varphi)=\frac{y}{r}[/tex]. $${z=r(\cos(\varphi)+i\sin(\varphi))}$$
Euler's formula [tex]z=r \cdot e^{i\varphi}[/tex], where [tex]e^{i\varphi}=\cos(\varphi)+i\sin(\varphi)[/tex].

Multiplication of complex numbers in a trigonometric form $${z_1 \cdot z_2=r_1 \cdot r_2(\cos(\varphi_1+\varphi_2)+i\sin(\varphi_1+\varphi_2))}$$
Division of complex numbers in a trigonometric form $${\frac{z_1}{z_2}=\frac{r_1}{r_2}(\cos(\varphi_1-\varphi_2)+i\sin(\varphi_1-\varphi_2))}$$
Power of complex numbers in a trigonometric form $${z^n=r^n(\cos{n\varphi}+i\sin{n\varphi})}$$
Nth root of complex numbers in a trigonometric form $${\sqrt[n]{z}=\sqrt[n]{r} (\cos \frac{\varphi+2\pi k}{n}+i\sin \frac{\varphi+2\pi k}{n})}$$

Last time edited 2017-11-06

0

views 310

posts 0

active before 6 mo

 

If you want to write answers, you have to login!