Question

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. 2(cos 105 deg + i * sin 105 deg) )^ 3

Answer 1

First, we can convert the complex number to rectangular form:
2(cos 105° + i sin 105°) = 2(cos(105°) + i sin(105°)) = 2(0.2588 + 0.9659i) = 0.5176 + 1.9318i

Now, we can use DeMoivre's Theorem to find the cube of this complex number:
(r(cos θ + i sin θ))^n = r^n(cos nθ + i sin nθ)

So, we have:
(0.5176 + 1.9318i)^3 = (2.0144 - 1.9416i)

Therefore, the indicated power of the complex number is (2.0144 - 1.9416i) in rectangular form.