Question

Which expression represents a cube root of 1 + I?

Answer 1

The expression that represents the cube root of 1 + i is: ∛(sqrt(2)) * (cos(15°) + i sin(15°))

Step-by-step explanation:

The expression that represents the cube root of 1 + i is:

∛(1 + i)

To simplify this expression, we can first convert the complex number 1 + i to polar form.

1 + i = r(cos(θ) + i sin(θ))

where r = sqrt(1^2 + 1^2) = sqrt(2) and θ = arctan(1/1) = 45°

Now, we can write the cube root of 1 + i as:

∛(sqrt(2) * (cos(45°) + i sin(45°)))

Using the properties of complex numbers and De Moivre's theorem, we can simplify this expression:

∛(sqrt(2)) * (cos(45°/3) + i sin(45°/3))

The final expression is:

∛(sqrt(2)) * (cos(15°) + i sin(15°))

Answer 2

D (I think!!)

Step-by-step explanation:

I searched for a complex plane graph and put in each answer and this was the closest.