Let z_1 and z_2 be two distinct complex
numbers and let z = (1 − t)z_1 + tz_2 for
some real number t with 0 < t < 1. If
arg(w) denotes the principal argument
of a non-zero complex number w, then
(1) ∣z − z_1 ∣ + ∣z − z_2 ∣ = ∣z_1 − z_2 ∣
(2) Arg (z − z_1 ) = Arg (z − z_2 )
(3) determinant (((z − z_1 ),(z^ − z_1 ^ )),((z_2 − z_1 ),(z_2 ^ − z_1 ^ ))) = 0
(4) Arg (z − z_1 ) = Arg (z_2 − z_1 )
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