De Moivre's Theorem Formula:
The de Moivre theorem explains how to calculate the powers of complex numbers.
For any complex number x and any integer n,
(cos x + i sin x)n = cos(nx) + isin (nx)
How to Use De Moivre’s Theorem Calculator?
- Enter the complex number z into the calculator. Complex numbers are typically written in the form a + bi, where a is the real part and b is the imaginary part. For example, the complex number 3 + 4i would be entered as 3+4i.
- Enter the positive integer n into the calculator. This is the power to which you want to raise the complex number z.
- Click the "Calculate" button to compute (zn) based on De Moivre's Theorem.
- The calculator will display the result in both polar and rectangular form. The polar form of a complex number is written as (r, θ), where r is the modulus (magnitude) of the number and θ is the argument (angle) in polar coordinates. The rectangular form of a complex number is written as a + bi, where a is the real part and b is the imaginary part.
For example, if you entered the complex number 3 + 4i and the integer 3 into the calculator, the result would be displayed as (5, 0.93) in polar form and -7+24i in rectangular form.