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Let z be any non-zero complex number. Th...

Let z be any non-zero complex number. Then pr. arg(z) + pr.arg`(barz)` is equal to

A

`pi`

B

`-pi`

C

0

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
C
Following cases arise:
Case I When point representing z lies in first or fourth quadrant:
In this case, if pr.arg(z)=`alpha`, then pr.arg`(barz)=-alpha`, where `tanalpha=("lm"(z))/|("Re"(z))|`
`therefore` pr.arg(z)+pr.arg`(barz)=0`
Case II: When point representing z lies in the second or fourth quadrant.
If `pr. arg(z) =-(pi-alpha)=pi-alpha`.
Hence, in all the cases, `pr. arg(z) + arg(z)+pr.argbar(z)=0`.
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