Mathegoras

Complex numbers › The complex plane › Argument and polar form

Argument of a sum of cis terms

High school · ●●●○○ 50 pts

The number cis⁡75∘+cis⁡83∘+cis⁡91∘+⋯+cis⁡147∘\operatorname{cis} 75^\circ + \operatorname{cis} 83^\circ + \operatorname{cis} 91^\circ + \dots + \operatorname{cis} 147^\circ is expressed in the form rcis⁡θr \operatorname{cis} \theta, where r>0r > 0 and 0∘≤θ<360∘0^\circ \le \theta < 360^\circ. Find θ\theta in degrees.

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polar formarithmetic sequences