QUICK HELP ????!

Question

Find the product Z1=1/2(cis pi/3) and z2=3(cos pi/6+ i sinpi/6)

then place your answer in rectangular form

show work please

Answer 1

z₁z₂ = r₁r₂[cos(θ₁+θ₂)+i·sin(θ₁+θ₂)]

z₁z₂ = (1/2)(3)[cos(π/3+π/6)+i·sin(π/3+π/6)]

z₁z₂ = (3/2)[cos(π/2)+i·sin(π/2)]

z₁z₂ = (3/2)(0+i)

z₁z₂ = (3/2)i

Hope this helped! This is probably an easier method to solve the problem than in the other answer.

Answer 2

cis(π/3)/2 = (cos(π/3)+isin(π/3))/2 = 1/4+i√3/4

3(cos(π/6)+isin(π/6)) = 3√3/2+3i/2

(1/4+i√3/4)(3√3/2+3i/2) = 3√3/8+3i/8+9i/8-3√3/8 =(3/2)i=1.5i