Let \( z_{1} \) and \( z_{2} \) be two distinct complex numbers and...

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Let \( z_{1} \) and \( z_{2} \) be two distinct complex numbers and \( z=(1-t) z_{1}+i z_{2} \), for some real number \( t \) with \( 0t1 \)
\( \mathrm{P} \) and \( i=\sqrt{-1} \). If \( \arg (w) \) denotes the principal argument

W of a non-zero complex number \( w \), then [IIT-JEE 2010, 3M]
(a) \( \left|z-z_{1}\right|+\left|z-z_{2}\right|=\left|z_{1}-z_{2}\right| \)
(b) \( \arg \left(z-z_{1}\right)=\arg \left(z-z_{2}\right) \)
(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) \( \arg \left(z-z_{1}\right)=\arg \left(z_{2}-z_{1}\right) \)
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