MCQ
Choose the correct answer.
If $\Big(\frac{1+\text{i}}{1-\text{i}}\Big)^{\text{x}}=1,$ then:
If $\Big(\frac{1+\text{i}}{1-\text{i}}\Big)^{\text{x}}=1,$ then:
- Ax = 2n + 1
- Bx = 4n
- Cx = 2n
- Dx = 4n + 1, where n ∈ N
Solution:
$\Rightarrow\Big[\frac{(1+\text{i})(1+\text{i})}{(1-\text{i})(1+\text{i})}\Big]^{\text{x}}=1$
$\Rightarrow\Big[\frac{1+2\text{i}+\text{i}^2}{1-\text{i}^2}\Big]^{\text{x}}=1$
$\Rightarrow\Big[\frac{2\text{i}}{1+1}\Big]^{\text{x}}=1$
$\Rightarrow\text{i}^{\text{x}}=1$
$\Rightarrow\text{x}=4\text{n},\text{n}\in\text{N}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
The value of $\tan75^\circ-\cot75^\circ$ is equal to:
$2\sqrt{3}$
$2+\sqrt{3}$
$2-\sqrt{3}$
$1$
150
-50
-150
50