MCQ
The argument of $\frac{1-\text{i}}{1+\text{i}}$ is:
- A$-\frac{\pi}{2}$
- B$\frac{\pi}{2}$
- C$\frac{3\pi}{2}$
- D$\frac{5\pi}{2}$
Solution:
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, $\text{arg(z)}=\frac{-\pi}{2}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.