For z1=9cis(5π/6) and z2=3cis(π/3), find z1/z2 in rectangular form. A. -3

B. 3

C. -3i

D. 3i

D) 3 i

Step-by-step explanation:

Step(i):-

Given  Z₁ = 9 Cis ( 5π/6) = 9 ( Cos (5π/6) +i Sin (5π/6))

          Z₂ = 3 Cis ( π/3) = 3 ( Cos (π/3) +i Sin (π/3))

  Now  Cos (5π/6) = cos (150°) = cos(90°+60°)   = -sin 60 =

           Sin (5π/6) = Sin (150°) = Sin(90°+60°)   = Cos 60 =

    Z₁  = 9 ( Cos (5π/6) +i Sin (5π/6))

   Z₂ = 3 ( Cos (π/3) +i Sin (π/3))    

Step(ii):-

Rationalize with 1 - i √3 and we get

on simplification , we will use formulas

i² = -1 and    (a+b)(a-b) = a² - b²

Final answer:-

D. 3i

Step-by-step explanation: I got this right on Edmentum.

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632