Math.
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De Moivre s Theorem
Know More About :- Properties of Rational Number
De Moivre s Theorem
In mathematics, de Moivre s formula (a.
k.
a.
De Moivre s theorem and De Moivre s identity), named
after Abraham de Moivre, states that...
More
Math.
Edurite.
com Page : 1/3
De Moivre s Theorem
Know More About :- Properties of Rational Number
De Moivre s Theorem
In mathematics, de Moivre s formula (a.
k.
a.
De Moivre s theorem and De Moivre s identity), named
after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x
and integer n it holds that
( cos x + isin x )n = cos(nx) + isin(nx).
While the formula was named after De Moivre, he never explicitly stated it in his works.
The formula is
important because it connects complex numbers (i stands for the imaginary unit (i2 = −1.
)) and
trigonometry.
The expression cos x + i sin x is sometimes abbreviated to cis x.
By expanding the left
hand side and then comparing the real and imaginary parts under the assumption that x is real, it is
possible to derive useful expressions for cos (nx) and sin (nx) in terms of cos x and sin x.
Furthermore,
one can use a generalization of this formula to find explicit expressions for the nth roots of
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