Question

"Please help

Evaluate and write your answer in a + bi form, rounding to 2 decimal places if needed. [2(cos 58° + i sin 58*)]^3

Answer 1

To evaluate the expression [2(cos 58° + i sin 58°)]^3 in the form a + bi, we can apply De Moivre's theorem. The result, rounded to 2 decimal places, is -7.68 - 1.72i.

Step-by-step explanation:

To evaluate the expression [2(cos 58° + i sin 58°)]^3 in the form a + bi, we can use De Moivre's theorem for exponentiation of complex numbers.

De Moivre's theorem states that (r(cos θ + i sin θ))^n = r^n (cos nθ + i sin nθ).

Applying De Moivre's theorem to our expression, we have:

(2(cos 58° + i sin 58°))^3 = 2^3 (cos (3 * 58°) + i sin (3 * 58°))

Calculating the angle: 3 * 58° = 174°

Rounding to 2 decimal places, the result is: 8(cos 174° + i sin 174°) = 8(cos 180° - 6° + i sin 180° - 6°) = -7.68 - 1.72i

Answer 2

To evaluate the expression [2(cos 58° + i sin 58°)]^3, we can use De Moivre's Theorem. By simplifying the expression using De Moivre's Theorem, we find that the answer is 8.00(cos 174° + i sin 174°).

Step-by-step explanation:

To evaluate the expression [2(cos 58° + i sin 58°)]^3 in the form a + bi, we'll use De Moivre's Theorem. De Moivre's Theorem states that (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ).

Using this theorem, we can rewrite [2(cos 58° + i sin 58°)]^3 as 2^3 * (cos (3 * 58°) + i sin (3 * 58°)).

Simplifying further, we have 8(cos 174° + i sin 174°). Therefore, the answer is 8.00(cos 174° + i sin 174°).