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 nonzero complex number w, then

JEE Advanced 2010 Mathematics question

Let and be two distinct complex numbers and let for some real number t with . If Arg(w) denotes the principal argument of a nonzero complex number w, then

(A)Correct
(B)
(C)Correct
(D)Correct

Answer: (A),(C),(D)

Solution

with is a point lying strictly between and on the segment joining them. We have and . (A) : true. (B) is a positive multiple of

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Question ID VK-025772