Explanation

(d)
For collinear points $\left| \begin{matrix}
z_{1} & \overline{z_{1}} & 1 \\
z_{2} & \overline{z_{2}} & 1 \\
z_{3} & \overline{z_{3}} & 1
\end{matrix} \right| = 0$
$\therefore\ \ \ \ \left| \begin{matrix}
1 + 2i & 1 - 2i & 1 \\
2 + 3i & 2 - 3i & 1 \\
3 + 4i & 3 - 4i & 1
\end{matrix} \right| = \left| \begin{matrix}
4i & 1 - 2i & 1 \\
6i & 2 - 3i & 1 \\
8i & 3 - 4i & 1
\end{matrix} \right|\lbrack C_{1} \rightarrow C_{1} - C_{2}\rbrack$
$= \left| \begin{matrix}
- 2i & - 1 + i & 0 \\
- 2i & - 1 + i & 0 \\
8i & 3 - 4i & 1
\end{matrix} \right| = 0$
$\lbrack R_{1} \rightarrow R_{1} - R_{2},\ \ \ R_{2} \rightarrow R_{2} - R_{3}\rbrack$