Q.

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

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a

z−z1+z−z2=z1−z2

b

arg⁡z−z1=arg⁡z−z2

c

z−z1z¯−z¯1z2−z1z¯2−z¯1=0

d

arg⁡z−z1=arg⁡z2−z1

answer is A.

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Detailed Solution

Given z=(1−t)z1+tz2(1−t)+tClearly, z divides z, and z, in the ratio of t :(1 - t), 0
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Let z1 and z2, be two distinct complex numbers and let z=(1−t)z1+t z2 for some real number t with 0 <  t < 1. if arg (w) denotes the principal argument of a non-zero complex number , then