Números Complejos

$$i = \sqrt{-1}$$

$$i^2 = -1$$

$$i^3 = -i$$

$$i^4 = 1$$

$$\sqrt{-a} = i\sqrt{a}, a\geq 0$$

$$(a+bi)+(c+di) = a + c + (b + d)i$$

$$(a+bi)-(c+di) = a - c + (b - d)i$$

$$(a+bi)(c+di) = ac - bd + (ad + bc)i$$

$$(a+bi)(a-bi) = a^2 + b^2$$

$$|a+bi| = \sqrt{a^2 + b^2}$$

$$\overline{(a+bi)} = a - bi$$

$$\overline{(a+bi)}(a+bi) = |a - bi|^2$$

$$\frac{1}{a+bi} = \frac{a - bi}{(a+bi)(a-bi)} = \frac{a-bi}{a^2 + b^2}$$