The value of the angle θ in the rcis θ be 16 degrees.
Given, a number rcis θ, is expressed by
cis 75° + cis 83° + cis 91° + ⋯ + cis 147°
we have to find the value of θ in degrees
Now, we have to find the sum of the given expression
cis 75° + cis 83° + cis 91° + ⋯ + cis 147°
as, cis θ = e^iθ
e^i75° + e^i83° + e^i91° + ⋯ + e^i147°
e^i75π/180 + e^i83π/180 + e^i91π/180 + ⋯ + e^i147π/180
On using the geometric sum of the Geometric Progression, we get
Sum = e^i75π/180(1 - e^i72π/180)/(1 - ei^8π/180)
r cis θ = cos θ + i sin θ
θ = 16°
The value of the angle θ be 16 degrees.
Hence, the value of the angle be 16 degrees.
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