Question

Q7 Q27.) Find zw. Leave your answer in polar form.

Answer 1

To multiply complex numbers in polar form: multiply the r parts and add the angle parts. Or

r1​(cos θ1​ + i sin θ1​) × r2​(cos θ2​ + i sin θ2​)

= r1​r2​(cos(θ1​+θ2​) + i sin(θ1​+θ2​))

so zw

=3*8(cos(π/9+π/12) + i sin(π/9+π/12))

=24(cos(7/36)π + i sin(7/35)π)

Answer 2

r1​(cosθ1​+isinθ1​)*r2​(cosθ2​+isinθ2​)

= r1​*r2*​(cos(θ1​+θ2​)+isin(θ1​+θ2​))

so zw

=3(cos(pi/9)+isin(pi/9))*8(cos(pi/12)+isin(pi/12))

=3*8*(cos(pi/9+pi/12)+isin(pi/9+pi/12))

=24(cos(7/36)pi+isin(7/35)pi)