1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let z = $\frac{1+\text{i}\sin \theta}{1−\text{i}\sin \theta}$ where i = $\sqrt{−1}$

What is angle θ such that z is purely real ?

where n is an integer

A
$\frac{n\pi}{2}$
B
$\frac{(2n+1)\pi}{2}$
C
D
2nπ only
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let z = $\frac{1+\text{i}\sin \theta}{1−\text{i}\sin \theta}$ where i = $\sqrt{−1}$

What is angle θ such that z is purely imaginary ?

where n is an integer

A
$\frac{n\pi}{2}$
B
$\frac{(2n+1)\pi}{2}$
C
D
2nπ
3
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the principal argument of $\frac{1}{1 + i}$ where $i = \sqrt{-1}?$
A
$-\frac{3\pi}{4}$
B
$-\frac{\pi}{4}$
C
$\frac{\pi}{4}$
D
$\frac{3\pi}{4}$
4
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the modulus of $\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}?$
A
$\frac{1}{4}$
B
$\frac{1}{2}$
C
1
D
2200
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