- #1
chaoseverlasting
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Can someone explain the De Moivre's Theorem and how its used to evaluate integrals of the type [tex]\int sin^mxcos^nxdx[/tex]
You can use Identites such as [tex]\cos^4 x = \frac{\cos 4x + 4\cos 2x +3}{8}[/tex] which can be derived from expanding the LHS of the theorem, to make the integrals easy.
De Moivre's Theorem:
[tex](\cos x + i \sin x)^n = \cos nx + i \sin nx[/tex]
Proof by induction or Euler's Formula.
Explain it? There it is, no intuitive feel or understanding about it, not unless you're Gauss.
Really? I beg to differ.
Raising a complex number of modulus 1 to the n'th power multiplies the argument by n. It is saying that multiplication of (unit) complex numbers gives rotations of the complex plane.
Really? I beg to differ.
Raising a complex number of modulus 1 to the n'th power multiplies the argument by n. It is saying that multiplication of (unit) complex numbers gives rotations of the complex plane.