Answer:
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
