Complex Power/Examples/2^i
Jump to navigation
Jump to search
Example of Complex Power
- $2^i = \map \cos {\ln 2} + i \map \sin {\ln 2}$
Proof
| \(\ds 2^i\) | \(=\) | \(\ds \map \exp {i \ln 2}\) | Definition of Complex Power | |||||||||||
| \(\ds \) | \(=\) | \(\ds \map \cos {\ln 2} + i \map \sin {\ln 2}\) | De Moivre's Formula |
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 4$. Elementary Functions of a Complex Variable: Exercise $6 \ \text{(iii)}$