De Moivre's theorem is a mathematical formula that expresses the power of a complex number in terms of its magnitude and angle. It is commonly used in fields such as physics, engineering, and finance.
The formula for De Moivre's theorem is (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ), where θ is the angle and n is the power.
De Moivre's theorem allows us to simplify complex number calculations by expressing powers in terms of trigonometric functions. It is also used in solving problems involving periodic functions and in the study of waves.
Yes, De Moivre's theorem can be applied to any complex number, as long as the number is written in the form a + bi, where a and b are real numbers and i is the imaginary unit.
De Moivre's theorem is used in various real-life applications, such as in electrical engineering for analyzing alternating currents, in physics for calculating the amplitude and phase of a wave, and in finance for calculating compound interest.