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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

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

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
z-z1=t(z2-z1)
\left | z-z1 \right |=t\left | z2-z1 \right |=t\left | z1-z2 \right |....(1)
z-z2=(1-t)(z1-z2)
\left |z-z2 \right |=(1-t)\left |(z1-z2) \right |=(1-t)\left |z2-z1 \right |....(2)
from 1 and 2 we get
\left | z-z1 \right |+\left | z-z2 \right |=\left | z2-z1 \right |
also arg(z-z1)=arg(z2-z1) since z1,z2,z lie on same straight line and on same side of z1.
Thanks and Regards
Shaik Aasif
askIITians Faculty

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