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.
Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u
faruk
what are the modern trends in religious behaviours
shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society
Lucius
that is how i understood it
Lucius
examples of societal norms
Diamond
Discuss the characteristics of the research located within positivist and the interpretivist paradigm