De Moivre's Theorem states that for any real number x and integer n, [cos(x) + i sin(x)]^n = cos(nx) + i sin(nx).

We can apply this theorem to the given problem as follows:

Given: [2(cos 20° + i sin 20°)]^3

Step 1: Apply De Moivre's Theorem
= 2^3 [cos(3*20°) + i sin(3*20°)]
= 8 [cos(60°) + i sin(60°)]

Step 2: Evaluate the trigonometric functions
= 8 [1/2 + i * sqrt(3)/2]
= 4 + 4i sqrt(3)

So, [2(cos 20° + i sin 20°)]^3 = 4 + 4i sqrt(3) in standard form.

Question

De Moivre's Theorem states that for any real number x and integer n, [cos(x) + i sin(x)]^n = cos(nx) + i sin(nx).

We can apply this theorem to the given problem as follows:

Given: [2(cos 20° + i sin 20°)]^3

Step 1: Apply De Moivre's Theorem
= 2^3 [cos(3*20°) + i sin(3*20°)]
= 8 [cos(60°) + i sin(60°)]

Step 2: Evaluate the trigonometric functions
= 8 [1/2 + i * sqrt(3)/2]
= 4 + 4i sqrt(3)

So, [2(cos 20° + i sin 20°)]^3 = 4 + 4i sqrt(3) in standard form.

Knowee AI · Accepted Answer

De Moivre's Theorem states that for any real number x and integer n, [cos(x) + i sin(x)]^n = cos(nx) + i sin(nx).

We can apply this theorem to the given problem as follows:

Given: [2(cos 20° + i sin 20°)]^3

Step 1: Apply De Moivre's Theorem
= 2^3 [cos(3*20°) + i sin(3*20°)]
= 8 [cos(60°) + i sin(60°)]

Step 2: Evaluate the trigonometric functions
= 8 [1/2 + i * sqrt(3)/2]
= 4 + 4i sqrt(3)

So, [2(cos 20° + i sin 20°)]^3 = 4 + 4i sqrt(3) in standard form.

Use de Moivre's Theorem to find the following. Write your answer in standard form.[2(cos 20° + i sin 20°)]3