DeMoivere’s Theorem

De Moivre's Theorem states that for a complex number $z=r(\cos {\theta }+i\sin {\theta })$ and integer Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n } , then

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [r(\cos{\theta} + i\sin{\theta})]^n = r^n(\cos{(n\theta)} + i\sin{(n\theta}))} .

Resources

• De Moivre’s Theorem. Written notes created by Professor Esparza, UTSA.
• Application of DeMoivre's Theorem. Produced by Professor Zachary Sharon, UTSA.
• De Moivre's Theorem and Powers of Complex Numbers, Mathematics LibreTexts