For a complex number z , If arg z ∈ - π , π , then arg 1 + cos ⁡ 6 π 5 + i sin ⁡ 6 π 5 is (here i 2 = - 1 )

Step-by-step solution

Let, z = 1 + cos ⁡ 6 π 5 + i sin ⁡ 6 π 5 = 2 cos ⁡ 3 π 5 cos ⁡ 3 π 5 + i sin ⁡ 3 π 5 = - 2 cos ⁡ 3 π 5 - cos ⁡ 3 π 5 - i sin ⁡ 3 π 5 = - 2 cos ⁡ 3 π 5 cos ⁡ 3 π 5 - π + i sin ⁡ 3 π 5 - π i.e. ω = - 2 cos ⁡ 3 π 5 cos ⁡ - 2 π 5 + i sin ⁡ - 2 π 5 Hence, arg z = - 2 π 5