CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
MCQ
The argument of $\frac{1-\text{i}}{1+\text{i}}$ is:
✓
$-\frac{\pi}{2}$
B
$\frac{\pi}{2}$
C
$\frac{3\pi}{2}$
D
$\frac{5\pi}{2}$
✓
Answer
Correct option: A.
$-\frac{\pi}{2}$
Let $\text{z}=\frac{1-\text{i}}{1+\text{i}}$
$\Rightarrow\text{z}=\frac{1-\text{i}}{1+\text{i}}\times\frac{1-\text{i}}{1-\text{i}}$
$\Rightarrow\text{z}=\frac{1+\text{i}^2-2\text{i}}{1-\text{i}^2}$
$\Rightarrow\text{z}=\frac{1-1-2\text{i}}{1+1}$
$\Rightarrow\text{z}=\frac{-2\text{i}}{2}$
$\Rightarrow\text{z}=\text{i}$
Since, $z$ lies on negative direction of imaginary axis.
Therefore, $\text{arg(z)}=\frac{-\pi}{2}$
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