Finding powers of complex numbers is greatly simplified using
De Moivre’s Theorem . It states that, for a positive integer
is found by raising the modulus to the
power and multiplying the argument by
It is the standard method used in modern mathematics.
De moivre’s theorem
If
is a complex number, then
where
is a positive integer.
Evaluating an expression using de moivre’s theorem
Evaluate the expression
using De Moivre’s Theorem.
Since De Moivre’s Theorem applies to complex numbers written in polar form, we must first write
in polar form. Let us find
Then we find
Using the formula
gives
Use De Moivre’s Theorem to evaluate the expression.
To find the
n th root of a complex number in polar form, we use the
Root Theorem or
De Moivre’s Theorem and raise the complex number to a power with a rational exponent. There are several ways to represent a formula for finding
roots of complex numbers in polar form.
The
n Th root theorem
To find the
root of a complex number in polar form, use the formula given as
where
We add
to
in order to obtain the periodic roots.
Questions & Answers
if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
