Write the value of arg(z)+arg (z) . - Vidyadip

Question

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

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Answer

Let z be a complex number with argument $\theta.$ Then, $\text{z}=\text{re}^{\text{i}\theta}$ $\Rightarrow\bar{\text{z}}=\overline{\text{re}^{\text{i}\theta}}=\text{re}^{-\text{i}\theta}$ ⇒ argument of $\bar{\text{z}}$ is $\theta.$ Thus, $\text{arg(z)}+\text{arg}\bar{(\text{z})}=0.$

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