如果θ∈(π/2,π)那么复数(1+i)(cosθ+isinθ)的辐角的主值是( )
A.θ+9π/4
B.θ+π/4
C.θ-π/4
D.θ+7π/4
复数(1+i)(cosθ+isinθ)=
(cos2
+isinπ 4
)(cosθ+isinθ)π 4
=
[cos(θ+2
)+isin(θ+π 4
)],π 4
∵θ∈(π/2,π)
复数(1+i)(cosθ+isinθ)的辐角的主值是:θ+π 4
故选B.
如果θ∈(π/2,π)那么复数(1+i)(cosθ+isinθ)的辐角的主值是( )
A.θ+9π/4
B.θ+π/4
C.θ-π/4
D.θ+7π/4
复数(1+i)(cosθ+isinθ)=
(cos2
+isinπ 4
)(cosθ+isinθ)π 4
=
[cos(θ+2
)+isin(θ+π 4
)],π 4
∵θ∈(π/2,π)
复数(1+i)(cosθ+isinθ)的辐角的主值是:θ+π 4
故选B.