1
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Read the information carefully and answer the given questions.

A complex number is given by $$z = {{1 + 2i} \over {1 - {{(1 - i)}^2}}}$$.
What is the principal argument of z?
A
0
B
$${\pi \over 4}$$
C
$${\pi \over 2}$$
D
$$\pi $$
2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $z$ is any complex number and $i z^3+z^2-z+i=0$, where $i=\sqrt{-1}$, then what is the value of $(|z|+1)^2$ ?
A

1

B

4

C

81

D

121

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If $x, y$ and $z$ are the cube roots of unity, then what is the value of $xy + yz + zx$?

A

0

B

1

C

2

D

3

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, then what is $\operatorname{Re} \left(\frac{z_1}{z_2}\right) + 1$ equal to?

A

$-1$

B

$0$

C

$1$

D

$5$

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