Multiplying and Dividing Complex Numbers

z_{1} = a_{1} + i b_{1}; a_{1}, b_{1} \in ℝ, i = \sqrt{- 1}

z_{2} = a_{2} + i b_{2}; a_{2}, b_{2} \in ℝ, i = \sqrt{- 1}

r_{1} = \sqrt{{a_{1}}^{2} + {b_{1}}^{2}}; r_{2} = \sqrt{{a_{2}}^{2} + {b_{2}}^{2}}

t g φ_{1} = \frac{b_{1}}{a_{1}} (a_{1} \neq 0); t g φ_{2} = \frac{b_{2}}{a_{2}} (a_{2} \neq 0)

Multiplying Complex Numbers

z_{1} \cdot z_{2} = (a_{1} \cdot a_{2} - b_{1} \cdot b_{2}) + i \cdot (a_{1} \cdot b_{2} + a_{2} \cdot b_{1})

z_{1} \cdot z_{2} = r_{1} \cdot r_{2} [\cos (φ_{1} + φ_{2}) + i \cdot \sin (φ_{1} + φ_{2})]

\frac{z_{1}}{z_{2}} = \frac{r_{1}}{r_{2}} [\cos (φ_{1} - φ_{2}) + i \cdot \sin (φ_{1} - φ_{2})]

Keywords: multiplying, dividing complex numbers