 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 (1i)^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 (1i)^2i = 2^ie^1.570796.
