Let C be the set of all complex numbers and C0 be the set of all no-ze – InterviewSolution

1.	Let C be the set of all complex numbers and C0 be the set of all no-zero complex numbers. Let a relation R on C0 be defined as z1 R z2 ⇔ z1-z2z1+z2 is real for all z1, z2 ∈C0.Show that R is an equivalence relation.
Answer» Let C be the set of all complex numbers and C₀be the set of all no-zero complex numbers. Let a relation R on C₀be defined as $z_{1}$ R $z_{2} \Leftrightarrow \frac{z_{1} - z_{2}}{z_{1} + z_{2}}$ is real for all $z_{1}, z_{2} \in$ C₀. Show that R is an equivalence relation.

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