6 - 2 4 + 6 + 2 4 i 2020 =

Step-by-step solution

Given: 6 - 2 4 + i 6 + 2 4 2020 [ As we know   sin 5 π 12 = 3 + 1 2 2 = 6 + 2 4 ,   cos 5 π 12 = 6 - 2 4 ] = cos 5 π 12 + i sin 5 π 12 2020 As we know ,   cos θ ± sin θ n = cos n θ ± i sin n θ = cos 2020 × 5 π 12 + i   sin 2020 × 5 π 12 = cos 505 × 5 π 3 + i   sin 505 × 5 π 3 = cos 842 π - π 3 + i   sin 842 π - π 3 = cos π 3 - i   sin π 3 = 1