Complex Numbers · NDA previous year questions

2021 4 questions

1. Q242021 · 18 Apr 2021

   Consider the following in respect of a complex number $z$: 1. $\overline{(z^{-1})}=(\bar{z}{)}^{-1}$ 2. $z{z}^{-1}=|z{|}^2$ Which of the above is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: A

2. Q252021 · 18 Apr 2021

   1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate is a real number.

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: C

3. Q262021 · 18 Apr 2021

   What is the modulus of the complex number $i^{2n+1}(-i{)}^{2n-1}$, where $n\in \mathbf{N}$ and $i=\sqrt{-1}$?

   1. A.1
   2. B.$-1$
   3. C.$\sqrt{2}$
   4. D.2
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   Answer: A

4. Q552021 · 18 Apr 2021

   If $Z=1+i$, where $i=\sqrt{-1}$, then what is the modulus of $z+\frac{2}{z}$?

   1. A.1
   2. B.2
   3. C.3
   4. D.4
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   Answer: B