Given z1 and z2 below. Calculate z1/z2 and write your answer in rcistheta form.

z1=-3+3sqrt(3)i
z2=27i

  (2/9)cis(30°)

Step-by-step explanation:

We can express the two numbers in magnitude∠angle form, then find their ratio.

  |z1| = 3√((-1)² +(√3)²) = 3√4 = 6

  ∠z1 = arctan((3√3)/(-3)) = -arctan(√3) = 120°

  z2 = 27∠90°

So, the ratio is ...

  z1/z2 = (6∠120°)/(27∠90°) = (6/27)∠(120°-90°)

  z1/z2 = (2/9)∠30°

y -5 = (-1/4)(x + 8)

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. : )