Complex Numbers · NDA previous year questions

2015 9 questions

1. Q42015 · 27 Sept 2015

   If $z_1$ and $z_2$ are complex numbers with $|z_1|=|z_2|$, then which of the following is/are correct? 1. $z_1=z_2$ 2. Real part of $z_1$ = Real part of $z_2$ 3. Imaginary part of $z_1$ = Imaginary part of $z_2$ Select the correct answer using the code given below:

   1. A.1 only
   2. B.2 only
   3. C.3 only
   4. D.None
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   Answer: D

2. Q52015 · 27 Sept 2015

   If the point $z_1=1+i$ where $i=\sqrt{-1}$ is the reflection of a point $z_2=x+iy$ in the line $i\bar{z}-iz=5$, then the point $z_2$ is

   1. A.$1+4i$
   2. B.$4+i$
   3. C.$1-i$
   4. D.$-1-i$
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   Answer: A

3. Q62015 · 19 Apr 2015

   If $$z=\frac{-2(1+2i)}{3+i}$$ where $i=\sqrt{-1}$, then the argument $\theta (-\pi <\theta \le \pi )$ of $z$ is

   1. A.$\frac{3\pi }{4}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{5\pi }{6}$
   4. D.$-\frac{3\pi }{4}$
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   Answer: D

4. Q72015 · 19 Apr 2015

   If $1,\omega ,{\omega }^2$ are the cube roots of unity, then the value of $$(1+\omega )(1+{\omega }^2)(1+{\omega }^4)(1+{\omega }^8)$$ is

   1. A.$-1$
   2. B.0
   3. C.1
   4. D.2
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   Answer: C

5. Q82015 · 19 Apr 2015

   What is the square root of $i$, where $i=\sqrt{-1}$?

   1. A.$\frac{1+i}{2}$
   2. B.$\frac{1-i}{2}$
   3. C.$\frac{1+i}{\sqrt{2}}$
   4. D.None of the above
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   Answer: C

6. Q92015 · 19 Apr 2015

   $(x^3-1)$ can be factorised as where $\omega$ is one of the cube roots of unity.

   1. A.$(x-1)(x-\omega )(x+{\omega }^2)$
   2. B.$(x-1)(x-\omega )(x-{\omega }^2)$
   3. C.$(x-1)(x+\omega )(x+{\omega }^2)$
   4. D.$(x-1)(x+\omega )(x-{\omega }^2)$
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   Answer: B

7. Q102015 · 19 Apr 2015

   What is $${\left[\frac{\sin \frac{\pi }{6}+i(1-\cos \frac{\pi }{6})}{\sin \frac{\pi }{6}-i(1-\cos \frac{\pi }{6})}\right]}^3$$ where $i=\sqrt{-1}$, equal to?

   1. A.1
   2. B.$-1$
   3. C.$i$
   4. D.$-i$
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   Answer: C

8. Q112015 · 19 Apr 2015

   What is the real part of $$(\sin x+i\cos x{)}^3$$ where $i=\sqrt{-1}$?

   1. A.$-\cos 3x$
   2. B.$-\sin 3x$
   3. C.$\sin 3x$
   4. D.$\cos 3x$
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   Answer: B

9. Q1162015 · 19 Apr 2015

   Consider the following statements in respect of the given equation : 1. All the roots of the equation are complex. 2. The sum of all the roots of the equation is 6. Which of the above statements 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: B