Write the Value of Arg ( Z ) + Arg ( ¯ Z ) . - Mathematics

Write the value of $\arg\left( z \right) + \arg\left( \bar{z} \right)$.

Solution

Let z be a complex number with argument θ.
Then,

$z = r e^{i\theta}$

$\Rightarrow \bar{z} = \bar{{r e^{i\theta}}} = r e^{- i\theta}$

⇒ argument of $\bar{z}$ is −θ.

Thus,

$\arg\left( z \right) + \arg\left( \bar{z} \right) = 0$.

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 17 | Page 63