求实数θ,使复数z = cos2θ + i(tan^2θ-tanθ-2)是：（1）实数（2）纯虚数
问题描述：
求实数θ,使复数z = cos2θ + i(tan^2θ-tanθ-2)是：（1）实数（2）纯虚数
答
z = cos2θ + i(tan^2θ-tanθ-2)
(1)实数
=>tan^2θ-tanθ-2 =0
(tanθ-2)(tanθ+1) =0
tanθ = 2 or -1
θ = arctan(2) or k(180°)-45° k =1,2,3,...,-1,-2,-3,.
（2）纯虚数
=>cos2θ = 0
θ = k(90°)+45° k=1,2,3,,-1,-2,...