若θ∈（-3π/4,-π/4)则复数z=(sinθ-cosθ）+（sinθ+cosθ）i在复平面内对应的点在哪个象限

题目

若θ∈（-3π/4,-π/4)则复数z=(sinθ-cosθ）+（sinθ+cosθ）i在复平面内对应的点在哪个象限

答案

z=(sinθ-cosθ）+（sinθ+cosθ）i
=根号2sin(θ-π/4)+(根号2sin(θ+π/4)）i
θ∈（-3π/4,-π/4)
θ-π/4∈（-π,-π/2)
根号2sin(θ-π/4)