Solução das Raízes Complexas do Cosh z = 1/2

Example 4 Acha estas as raizs complexas do Cosh z frac12 onde Cosh z fracC2 C22 Solução C2 C2 1 Rightarrow C2 C2 1 e2i heta e2i heta 1 cdot C2 C22 C2 1 0 Acordo na angulo Timos C2 frac12 fracsqrt32 So C2 frac12 fracsqrt32 lag C2 log frac12 fracsqrt32 lag1 ifracpi3 2Kpi K in mathbbZ ifracpi3 2Kpi Rightarrow sum ifracpi3 2Kpi K in mathbbZ C2 isqrt32 Rightarrow Z log isqrt32 Z ifracpi3 2Kpi K in mathbbZ As raizes complexas do Cosh frac12 Rightarrow Z ipm fracpi3 2Kpi K in mathbbZ