Complex NumbersHard

Question

Let z1 and z2 be two distinct complex numbers and let z = (1 - t) z1 + tz2 for some real number t with 0 < t < 1. If Arg (w) denotes the principal argument of a non-zero complex number w, then

Options

A.Arg (z - z1) = Arg (z - z2)
B.|z - z1| + |z - z2| = |z1 - z2|
C.= 0
D.Arg (z - z1) = Arg (z2 - z1)

Solution


Given z = (1 - t) z1 + tz2
⇒ = t ⇒ arg          .....(i)
⇒ arg (z - z1) = arg (z2 - z1)

AP + PB = AB 
⇒ |z - z1| + |z - z2| = |z1 - z2|.

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