| i | ||
Liczbe zespoloną z= | zapisz w postaci algebraicznej i trygonometrycznej | |
| 1−i |
| i(1+i) | i+i2 | i+(−1) | i−1 | |||||
z = | = | = | = | = | ||||
| (1−i)(1+i) | 12−i2 | 1−(−1) | 2 |
| 1 | 1 | |||
− | + | i. | ||
| 2 | 2 |
| 1 | 1 | 1 | ||||
|z| = ((− | )2+( | )2)1/2 = | , | |||
| 2 | 2 | √2 |
| 1 | 1 | 1 | ||||
z = | (− | + | i) | |||
| √2 | √2 | √2 |
| 1 | 1 | π | ||||
Kąterm, dla którego cosα=− | i jednocześnie sinα= | jest π− | , zatem | |||
| √2 | √2 | 4 |
| 1 | 3π | 3π | ||||
z = | (cos | +isin | ). | |||
| √2 | 4 | 4 |