z = x + yi i2 = −1 z = x + yi i2 = −1
$\text{sprz.\ }\overset{\overline{}}{z} = x - yi$ $\text{sprz.\ }\overset{\overline{}}{z} = x - yi$
$\text{mod\ }\left| z \right| = \sqrt{x^{2}{*y}^{2}}$ $\text{mod\ }\left| z \right| = \sqrt{x^{2}{*y}^{2}}$
pos tryg z = |z|(cosφ+isinφ) pos tryg z = |z|(cosφ+isinφ)
zn = |z|n(cos[nφ]+isin[nφ]) zn = |z|n(cos[nφ]+isin[nφ])
$\sqrt[n]{z} = \sqrt[n]{\left| z \right|}\left( \frac{\varphi + 2k\pi}{n} + isin\frac{\varphi + 2k\pi}{n} \right)$ $\sqrt[\text{\ n}]{z} = \sqrt[n]{\left| z \right|}\left( \frac{\varphi + 2k\pi}{n} + isin\frac{\varphi + 2k\pi}{n} \right)$
| ćw | I | II | III | IV |
|---|---|---|---|---|
φ= |
α0 |
π − α0 |
π + α0 |
2π − α0 |
| ćw | I | II | III | IV |
|---|---|---|---|---|
φ= |
α0 |
π − α0 |
π + α0 |
2π − α0 |
α0 |
0 | 30 | 45 | 60 | 90 |
|---|---|---|---|---|---|
| 0 | π/6 |
π/4 |
π/3 |
π/2 |
|
| |cos φ| | 1 | $$\frac{\sqrt{3}}{2}$$ |
$$\frac{\sqrt{2}}{2}$$ |
$$\frac{1}{2}$$ |
0 |
| |sin φ| | 0 | $$\frac{1}{2}$$ |
$$\frac{\sqrt{2}}{2}$$ |
$$\frac{\sqrt{3}}{2}$$ |
1 |
α0 |
0 | 30 | 45 | 60 | 90 |
|---|---|---|---|---|---|
| 0 | π/6 |
π/4 |
π/3 |
π/2 |
|
| |cos φ| | 1 | $$\frac{\sqrt{3}}{2}$$ |
$$\frac{\sqrt{2}}{2}$$ |
$$\frac{1}{2}$$ |
0 |
| |sin φ| | 0 | $$\frac{1}{2}$$ |
$$\frac{\sqrt{2}}{2}$$ |
$$\frac{\sqrt{3}}{2}$$ |
1 |
$A^{- 1} = \frac{1}{\text{detA}}D^{T}$ $A^{- 1} = \frac{1}{\text{detA}}D^{T}$
$crmr\ x = \frac{\det A_{x}}{\text{detA}}$ $crmr\ x = \frac{\det A_{x}}{\text{detA}}$
$\overrightarrow{a}o\overrightarrow{b} = |\overrightarrow{a}| \bullet |\overrightarrow{b|} \bullet \cos\left( \overrightarrow{a},\overrightarrow{b} \right) = a_{1}b_{1} + a_{2}b_{2} + a_{3}b_{3}$ $\overrightarrow{a}o\overrightarrow{b} = |\overrightarrow{a}| \bullet |\overrightarrow{b|} \bullet \cos\left( \overrightarrow{a},\overrightarrow{b} \right) = a_{1}b_{1} + a_{2}b_{2} + a_{3}b_{3}\backslash n\overrightarrow{a} \times \overrightarrow{b} = \left| \begin{matrix} \overrightarrow{i} & \overrightarrow{j} & \overrightarrow{k} \\ a_{1} & a_{2} & a_{3} \\ b_{1}\ & b_{2}\ & b_{3}\ \\ \end{matrix} \right|$ $\overrightarrow{a} \times \overrightarrow{b} = \left| \begin{matrix} \overrightarrow{i} & \overrightarrow{j} & \overrightarrow{k} \\ a_{1} & a_{2} & a_{3} \\ b_{1}\ & b_{2}\ & b_{3}\ \\ \end{matrix} \right|$