1
NDA 2018 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is $${i^{1000}} + {i^{1001}} + {i^{1002}} + {i^{1003}}$$ equal to (where, $$i = \sqrt { - 1} $$)?
A
0
B
i
C
$$-$$i
D
1
2
NDA 2018 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
The modulus-amplitude form of $$\sqrt 3 + i$$, where $$i = \sqrt { - 1} $$ is
A
$$2\left( {\cos {\pi \over 3} + i\sin {\pi \over 3}} \right)$$
B
$$2\left( {\cos {\pi \over 6} + i\sin {\pi \over 6}} \right)$$
C
$$4\left( {\cos {\pi \over 3} + i\sin {\pi \over 3}} \right)$$
D
$$4\left( {\cos {\pi \over 6} + i\sin {\pi \over 6}} \right)$$
3
NDA 2018 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is the value of the sum $$\sum\limits_{n = 2}^{11} {({i^n} + {i^{n + 1}})} $$, where $$i = \sqrt { - 1} $$?
A
i
B
2i
C
$$-$$ 2i
D
1 + i
4
NDA 2019 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$x = 1 + i$$, then what is the value of $${x^6} + {x^4} + {x^2} + 1$$?
A
6i $$-$$ 3
B
$$-$$6i + 3
C
$$-$$6i $$-$$ 3
D
6i + 3
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