Home › AP EAPCET (Engineering) › Mathematics › Algebra: De Moivre's Theorem › De Moivre's formula can be derived from Euler's …
De Moivre's formula can be derived from Euler's formula together with which law?
Athe triangle inequality
Bthe law of exponents
Cthe binomial theorem
Dthe law of sines
Answer & Solution
Correct answer: B. the law of exponents
Writing cos x + i sin x as e^(ix) and using (e^(ix))^n = e^(inx) gives the formula.
Related questions
The 9th power of cos 20° + i sin 20° is which value?Which is the hyperbolic analogue of de Moivre's formula?Which number satisfies the equation z^6 = 1?The formula for cos nx in powers of cos x is which classical polynomial family?De Moivre's formula links complex numbers with which branch of mathematics?Which method of proof is used to establish de Moivre's theorem for natural numbers?A non-integer power of a complex number gives what kind of result?For nonzero complex z, how many distinct values does z^(3/4) take?