For 'z_1 = 9"cis" (5pi) / (6) ' and 'z_2 = 3"cis" (pi) / (3) ', find ' (z1) / (z2) ' in rectangular form.

a) - 3

b) 3

c) - 3i

d) 3i

option D is correct, i. e. 3i

Step-by-step explanation:

Given are the complex number as Z₁ = 9 cis (5π/6) and Z₂ = 3 cis (π/3)

So magnitudes are r₁ = 9, and r₂ = 3

And arguments are ∅₁ = 5π/6, and ∅₂ = π/3

We know the formula for division of complex number is given as follows:-

If Z₁ = r₁ cis (∅₁) and Z₂ = r₂ cis (∅₂)

Then |Z₁ / Z₂| = (r₁/r₂) cis (∅₁ - ∅₂)

|Z₁ / Z₂| = (9/3) cis (5π/6 - π/3)

|Z₁ / Z₂| = 3 cis (5π/6 - 2π/6)

|Z₁ / Z₂| = 3 cis (3π/6)

|Z₁ / Z₂| = 3 cis (π/2)

|Z₁ / Z₂| = 3 cos (π/2) + 3i sin (π/2)

|Z₁ / Z₂| = 3 * (0) + 3i * (1)

|Z₁ / Z₂| = 0 + 3i

|Z₁ / Z₂| = 3i

Hence, option D is correct, i. e. 3i