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Let R be the relation defined on set of all complex numbers C as `z_(1)Rz_(2) hArr |z_(1)|=|z_(2)|` then 'R' is -

A

Reflexive

B

Symmetric

C

Transitive

D

Equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
D
`zRz rArr |z|=|z|` which is always true bence reflexice
`z_(1)Rz_(2) rArr |z_(1)| = |z_(2)| rArr |z_(2)| = |z_(1)|`
`rArr z_(1)Rz_(2)` hence symmetric
`z_(1)Rz_(2) rArr |z_(1)| = |z_(2)|` & `z_(2)Rz_(3)`
`rArr |z_(2)| = |z_(3)|` hence `|z_(1)| = |z_(3)|`
i.e., `z_(1)Rz_(3)` hence transitive so is equivalence relation.
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