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  • 求實(shí)數(shù)θ,使復(fù)數(shù)z = cos2θ + i(tan^2θ-tanθ-2)是:(1)實(shí)數(shù)(2)純虛數(shù)

    求實(shí)數(shù)θ,使復(fù)數(shù)z = cos2θ + i(tan^2θ-tanθ-2)是:(1)實(shí)數(shù)(2)純虛數(shù)
    數(shù)學(xué)人氣:427 ℃時(shí)間:2020-04-22 10:12:58
    優(yōu)質(zhì)解答
    z = cos2θ + i(tan^2θ-tanθ-2)
    (1)實(shí)數(shù)
    =>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)純虛數(shù)
    =>cos2θ = 0
    θ = k(90°)+45° k=1,2,3,,-1,-2,...
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