Question

How do you simplify `1/2(cos 2pi/3 + i sin 2pi/3) times 4(cos (pi/2) + i sin (pi/2))`?

Answer 1

see below

Explanation:

`1/2 (cos((2pi)/3)+i sin((2pi)/3)) * 4(cos(pi/2)+isin(pi/2))`

Use the formula `r_1 (cos⁡theta_1+i sin⁡ theta_1 )∙r_2 (cos⁡θ_2+i sinθ_2 )= r_1 r_2 [cos⁡(θ_1+θ_2 )+isin(θ_1+θ_2 )]`

`= 1/2 *4 [ cos (((2pi)/3)+pi/2) +i sin (((2pi)/3)+pi/2)]`

`=2[cos ((7pi)/6) + i sin ((7pi)/6)]`

`=2[-sqrt3/2+i(-1/2)]`

`=-sqrt3-i`