162 Complex coordinates; sensed angles; angles between lines Ch. 10
ProofWe use the notation of 10.6.1. In the case (10.6.1)z′=z 0 +zcisαso that
σ=
z′ 4 −z′ 3
z′ 2 −z′ 1
=
(z 4 −z 3 )cisα
(z 2 −z 1 )cisα
=ρ.
In the case (10.6.2)z′=z 0 + ̄zcisαso that
σ=
z′ 4 −z′ 3
z′ 2 −z′ 1
=
(z ̄ 4 −z ̄ 3 )cisα
(z ̄ 2 −z ̄ 1 )cisα
=ρ ̄.
10.8 Sensed angles of triangles, the sine rule ...............
10.8.1 .....................................
Definition. For any non-full angleθ, we denote byθFtheangleinA(F)such that
|θF|◦=|θ|◦.
O I
J H^1
H 2
H 4 H 3