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
问题描述:
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
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)