Which of the following is a third root of the given complex number.

The correct option is C.

Step-by-step explanation:

The given complex number is

We need to find the third root of the given complex number.

De moivre's theorem:

where, n is an integer.

Using de moivre's theorem, we get

Therefore the correct option is C.

Step-by-step explanation:

The third root of the number 64∠(π/7) will be ...

  64^(1/3) ∠((π/7 +2nπ)/3) . . . . for n = 0, 1, 2 (angles repeat after that)

  = 4 ∠((π/21)(1+14n)) . . . . . . . . for n = 0, 1, 2

  = 4∠(π/21), 4∠(15π/21), 4∠(29π/21)

Of these three third roots, only the first two are listed among the answer choices. In your preferred form, they are ...

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

1. perpendicular

2. parallel

3. perpendicular