12th Mathematics - Book Back Answers - Chapter 2 - English Medium Guides

  

 

Plus Two / 12th Mathematics - Book Back Answers - Chapter 2 - English Medium

Tamil Nadu Board 12th Standard Mathematics - Chapter 2: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 2 from the Tamil Nadu State Board 12th Standard Chemistry textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 2 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

 

Chapter 2 - Complex Numbers

I. Multiple Choice Questions

1. iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³  is
(1) 0 
(2) 1 
(3) −1 
(4) i
Answer Key:

2. The value of $\mathbf{\sum }_{\mathit{n}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}}^{\mathbf{13}}$ (iⁿ + i^n-1) is
(1) 1+ i 
(2) i 
(3) 1 
(4) 0
Answer Key:

3. The area of the triangle formed by the complex numbers z,iz, and z + iz in the
Argand’s diagram is
(1) $\frac{\mathbf{1}}{\mathbf{3}}$ |Z|² 

(2) |Z|²
(3) $\frac{\mathbf{3}}{\mathbf{2}}$ |Z|²
(4) 2 |Z|²
Answer Key:

4. The conjugate of a complex number is $\frac{\mathbf{1}}{\mathbf{i}\mathbf{-}\mathbf{2}}$. Then, the complex number is
(1) $\frac{\mathbf{1}}{\mathbf{i}\mathbf{+}\mathbf{2}}$
(2) $\frac{\mathbf{-}\mathbf{1}}{\mathbf{i}\mathbf{+}\mathbf{2}}$
(3) $\frac{\mathbf{-}\mathbf{1}}{\mathbf{i}\mathbf{-}\mathbf{2}}$
(4) $\frac{\mathbf{1}}{\mathbf{i}\mathbf{-}\mathbf{2}}$
Answer Key:

5. If z = $\frac{\mathbf{(}\sqrt{\mathbf{3}}\mathbf{+}\mathbf{i}{\mathbf{)}}^{\mathbf{3}}\mathbf{(}\mathbf{3}\mathbf{i}\mathbf{+}\mathbf{4}{\mathbf{)}}^{\mathbf{2}}}{\mathbf{(}\mathbf{8}\mathbf{+}\mathbf{6}\mathbf{i}{\mathbf{)}}^{\mathbf{2}}}$ , then | z | is equal to
(1) 0 
(2) 1 
(3) 2 
(4) 3
Answer Key:

6. If z is a non zero complex number, such that 2iZ²= $\overline{\mathbf{z}}$ then | z | is
(1) -2
(2) +2 
(3) 2 
(4) 3
Answer Key:

7. If | z- 2 + i | ≤ 2 , then the greatest value of | z | is
(1) $\sqrt{\mathbf{3}}$− 2 
(2) $\sqrt{\mathbf{3}}$+ 2 
(3) $\sqrt{\mathbf{5}}$− 2 
(4) $\sqrt{\mathbf{5}}$+ 2
Answer Key:

8. If z      , then the least value of | z | is
(1) 1 
(2) 2 
(3) 3 
(4) 5
Answer Key:

9. If | z |=1, then the value of $\frac{\mathbf{1}\mathbf{+}\mathbf{z}}{\mathbf{1}\mathbf{+}\overline{\mathbf{z}}}$ is
(1) z
(2) $\frac{\overline{\mathbf{z}}}{}$ 
(3) $\frac{\mathbf{1}}{\mathbf{z}}$
(4) 1
Answer Key:

10. The solution of the equation | z | - z = 1+2i is
(1) $\frac{\mathbf{3}}{\mathbf{2}}$-2i
(2) $\mathbf{-}\frac{\mathbf{3}}{\mathbf{2}}$+2i
(3) 2-$\mathbf{-}\frac{\mathbf{3}}{\mathbf{2}}\mathit{i}$
(4) 2+$+\frac{\mathbf{3}}{\mathbf{2}}i$
Answer Key:

11. If |Z₁| =1, |Z₂| = 2, Z₂| = 3 and |9Z₁Z₂ + 4Z₁Z₃ + Z₂Z₃| then the value of |Z₁ + Z₂ + Z₃| is
(1) 1 
(2) 2 
(3) 3 
(4) 4
Answer Key:

12. If z is a complex number such that z∈C \ R and $\mathbf{z}\mathbf{+}\frac{\mathbf{1}}{\mathbf{z}}$ ∈R, then | z | is
(1) 0 
(2) 1 
(3) 2 
(4) 3
Answer Key:

13. Z_1, Z_3, and Z₃ are complex numbers such that Z₁ + Z₂ + Z₃ = 0 and |Z₁| = Z₂| =  Z₂| =  1then
is
(1) 3 
(2) 2 
(3) 1 
(4) 0
Answer Key:

14. If $\frac{\mathbf{z}\mathbf{-}\mathbf{1}}{\mathbf{z}\mathbf{+}\mathbf{1}}$ is purely imaginary, then | z | is
(1) $\frac{\mathbf{1}}{\mathbf{2}}$
(2) 1 
(3) 2 
(4) 3
Answer Key:

15. If z = x+iy is a complex number such that | z+ 2 | = | z - 2 | , then the locus of z is
(1) real axis 
(2) imaginary axis 
(3) ellipse 
(4) circle
Answer Key:

16. The principal argument of $\frac{\mathbf{3}}{\mathbf{-}\mathbf{1}\mathbf{+}\mathbf{i}}$ is
(1) $\frac{\mathbf{-}\mathbf{5}\mathbf{\pi }}{\mathbf{6}}$
(2) $\frac{\mathbf{-}\mathbf{2}\mathbf{\pi }}{\mathbf{3}}$
(3) $\frac{\mathbf{-}\mathbf{3}\mathbf{\pi }}{\mathbf{4}}$
(4) $\frac{\mathbf{-}\mathbf{\pi }}{\mathbf{2}}$
Answer Key:

17. The principal argument of (sin 40° + i cos 40°)⁵ is
(1) -110°
(2) -70°
(3) 70° 
(4) 110°
Answer Key:

18. If (1+i)(1+2i)(1+3i)…(1+ni) = x+iy,  then 2.5.10.(1+n²)  is
(1) 1 
(2) i 
(3) x² + y²
(4) 1+n²
Answer Key:

19. If 𝛚≠1 1 is a cubic root of unity and (1+𝛚)⁷  = A+ B𝛚 , then (A, B) equals
(1) (1, 0) 
(2) (−1, 1) 
(3) (0, 1) 
(4) (1, 1)
Answer Key:

20. The principal argument of the complex number $\frac{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{i}\sqrt{\mathbf{3}}{\mathbf{)}}^{\mathbf{2}}}{\mathbf{4}\mathbf{i}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{i}\sqrt{\mathbf{3}}\mathbf{)}}$ is
(1) $\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{3}}$
(2) $\frac{\mathbf{\pi }}{\mathbf{6}}$
(3) $\frac{\mathbf{5}\mathbf{\pi }}{\mathbf{6}}$
(4) $\frac{\mathbf{\pi }}{\mathbf{2}}$
Answer Key:

21. If α and β are the roots of x² + x + 1 = 0, then α²⁰²⁰ + β²⁰²⁰ is
(1) −2 
(2) −1 
(3) 1 
(4) 2
Answer Key:

22. The product of all four values of

$($${\left(\mathbf{cos}\frac{\mathbf{\pi }}{\mathbf{3}}\mathbf{+}\mathbf{i} \mathbf{s}\mathbf{i}\mathbf{n}\frac{\mathbf{\pi }}{\mathbf{3}}\right)}^{\frac{\mathrm{}}{}}$$)$${\frac{3}{4}}^{}$ is

(1) −2 
(2) −1 
(3) 1 
(4) 2
Answer Key:

23. If _ _ 1 is a cubic root of unity and k , then k is equal to
(1) 1 
(2) −1 
(3) 3i 
(4) − 3i
Answer Key:

24. The value of 1 3 is
(1) 
(2) 
(3) 
(4) 
Answer Key:

25. If _ , then the number of distinct roots of
(1) 1 
(2) 2 
(3) 3 
(4) 4
Answer Key:

 

II.Short Answer Questions.

12th Mathematics

III. Long Answer Questions.

12th Mathematics

IV. Exercise.

12th Mathematics