Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. 2(cos20∘+isin20∘))3=

After solving the power:

Rectangular form:

Step-by-step explanation:

Given the complex number:

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

First of all, let us solve:

Let us apply the De Moivre's Theorem:

Here, n = 3

Now, the given complex number becomes:

Let us put the values of and

So, the rectangular form of the given complex number is:

45

step-by-step explanation: