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°

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1