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 Powers of Complex Numbers, DeMoivre's Theorem, a selection of answers from the Dr. Math archives. Usefulness of De Moivre's Theorem What is the usefulness of de Moivre's theorem? History of DeMoivre's Theorem What is the history behind DeMoivre's theorem - did he base it on the work of predecessors? DeMoivre's Formula Can you explain DeMoivre's Theorem? Square Roots of Complex Numbers Devise at least two methods for finding the square root of (a+bi). Proving De Moivre's Theorem Prove De Moivres theorem: - (cos(x)+isin(x))^n = cos(nx) + isin(nx). Proof of DeMoivre's Theorem A typical induction proof: DeMoivre's theorem. DeMoivre's Theorem: Standard Form Use DeMoivre's theorem to write (1-i)^10 in standard form. Exponentiation How do I calculate x^y using only exp, ln, log, and the trigonometric functions? Square Root of i Our algebra teacher asked us to find the square root of i. I applied the properties of exponents and got (-1)^(1/4). Trigonometric Identity Prove that sin 7x = 7(sin x) - 56(sin x)^3 + 112(sin x)^5 - (sin x)^7. Trigonometry and Complex Numbers Simplify (sqrt 3 - i)^7 into the form a + bi using DeMoivre's Theorem. Euler Equation and DeMoivre's Theorem Do you have a proof of the equation e^(i*Pi) + 1 = 0? de Moivre's Formula How do I use de Moivre's formula to express cos(3p) and sin(3p) in terms of cos p and sin p? And why would this be useful? Cosine 20 Degrees What is the exact value of cosine 20 degrees? Plotting Complex Numbers I cannot figure out (1-i)^2i = 2^ie^1.570796.