Write the value of
Question:

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

Solution:

Let z be a complex number with argument θ.

Then,

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

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

 

$\Rightarrow$ argument of $\bar{z}$ is $-\theta$

Thus, $\arg (z)+\arg (\bar{z})=0$.

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