Question

Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.

Answer 1

r1​(cosθ1​ + i sinθ1​) / r2(cosθ2 + i sinθ2​)​ = r1/​r2​​(cos(θ1−θ2​) + i sin(θ1​−θ2))

z1/z2

=3(cos(pi/8)+isin(pi/8)/7(cos(pi/9)+isin(pi/9)

=3/7(cos(pi/8-pi/9)+isin(pi/8-pi/9)

=3/7(cos(pi/72)+isin(pi/72)

Answer 2

To divide complex numbers in polar form, divide the r parts and subtract the angle parts. Or

r2​(cosθ2​ + i sinθ2​) / r1​(cosθ1 + i sinθ1​)​ = r2/​r1​​(cos(θ2−θ1​) + i sin(θ2​−θ1))

z1/z2

= 3/7 (cos(π/8-π/9) + i sin(π/8 - π/9))

= 3/7 (cos(π/72) + i sin(π/72))