Find the quotient, and write it in rectangular form (do not factor)

Question

(12(cos 420 + i sin 420)) / (2(cos 120 + i sin 120))

 

Thank you for your time. 

Answer 1

If z₁=12(cos420 + isin420)

and z₂ = 2(cos(120+isin120))    

z₁/z₂=r_{1 /} r_{2 [}cos(α_{1 -} α₂₎  + isin(α1 - α2) ]

α1 - α2

in your case r1= 12  and r2=2 and the α₁ = 420 and α_{2 = 120}

then z₁/z₂= (12/2)[cos(420-120) +isin(420-120)]  = 6[cos300 + isin300]= 6(1/2 -i√3/2) = 3 -3i√3