Complex Power/Examples/2^i

From ProofWiki
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