CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers1 Mark
Question
Write the value of $\text{arg(z)}+\text{arg}\bar{(\text{z})}.$
✓
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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