Question

Тригонометрическая и показательны форма , и номер 6

Answer 1

4

$z = 3 - 3i$

$|z| = sqrt{3^2 + (-3)^2} = 3sqrt{2} \begin{cases} cos arg z = frac{3}{3sqrt{2}} = frac{1}{sqrt{2}} \ sin arg z = frac{-3}{3sqrt{2}} = -frac{1}{sqrt{2}}end{cases} Rightarrow arg z = -frac{pi}{4}$

$z = 3sqrt{2} (cos(-frac{pi}{4}) + isin(-frac{pi}{4}))$

$e^{iphi} = cos(phi) + isin(phi) Rightarrow z = 3sqrt{2},e^{-frac{ipi}{4}}$

6

$Large displaystyle {int {frac{dx}{(5x + 13)^3}}} = Large displaystyle {frac{1}{5}int {frac{d(5x + 13)}{(5x + 13)^3}}} = begin{vmatrix}t = 5x + 13 \ dt = 5,dxend{vmatrix} = Large displaystyle {frac{1}{5}int {frac{dt}{t^3}}} =\= -frac{1}{10t^2} + C = -frac{1}{10(5x + 13)^2} + C$