Find the fifth roots of 32(cos 280° + i sin 280°)

The fifth root is 2[cos(56°) + i sin(56°)]

Step-by-step explanation:

* To solve this problem we must revise De Moiver's rule

- In the complex number with polar form

∵ z = r(cosФ + i sinФ)

∴ z^n = r^n(cos(nФ) + i sin(nФ))

* In the problem

- The fifth root means z^(1/5)

- We can put 32 as a form a^n

∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5

∴ z = 2^5[cos(280°) + i sin(280°)]

* Lets find z^(1/5)

∴ z^(1/5) = 2[cos(56) + i sin(56)]

* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]

step-by-step explanation:

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )