Iam not sure how to do this problem and need asap

  (2, 4π/15), (2, 14π/15), (2, 24π/15)

Step-by-step explanation:

DeMoivre's theorem tells you the n-th root of a complex number in polar form is ...

  (magnitude, angle)^(1/n) = (magnitude^(1/n), (angle +2kπ)/n) for k = 0 to n-1.

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Your number has a magnitude of 8, so the cube root of that is 2.

Your number has an angle of (4π/5+2kπ), so one third of that is ...

  (π/3)(4/5 +2k) . . . for k = 0, 1, 2

Then the cube roots are (magnitude, angle) ...

  {(2, 4π/15), (2, 14π/15), (2, 24π/15)}

Of course, you can write (magnitude, angle) in CIS form as ...

  magnitude(cos(angle) +i·sin(angle))

as may be required by your grader.

Comment on complex number notation

The notation used in my engineering courses was fairly practical. A complex number could be written as a+bi or as magnitude∠angle. We didn't waste effort writing it as magnitude(cos(angle) +i·sin(angle)) and we avoided the confusion associated with different interpretations of an ordered pair.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

18

step-by-step explanation:

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