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DeMoivre's Theorem

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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.

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.

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