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Complex Numbers question

2010 · Shift 1 · Q53

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2010 · Shift 1 · Q53

Complex Numbers question

2010 · Shift 1 · Q53

JEE AdvancedMathematicsComplex NumbersMultiple correct+3 / −1

Let

z_1

and

z_2

be two distinct complex numbers let

z=(1-t) z_1+t z_2

for some real number t with

0 If

\operatorname{Arg}(w)

denotes the principal argument of a nonzero complex number

w$, then :

A
$\left|z-z_1\right|+\left|z-z_2\right|=\left|z_1-z_2\right|$
B
$\operatorname{Arg}\left(z-z_1\right)=\operatorname{Arg}\left(z-z_2\right)$
C
$\left|\begin{array}{cc}z-z_1 & \bar{z}-\bar{z}_1 \\ z_2-z_1 & \bar{z}_2-\bar{z}_1\end{array}\right|=0$
D
$\operatorname{Arg}\left(z-z_1\right)=\operatorname{Arg}\left(z_2-z_1\right)$

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