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# NCERT solutions for Class 11 Mathematics chapter 5 - Complex Numbers and Quadratic Equations

## Chapter 5 - Complex Numbers and Quadratic Equations

#### Pages 103 - 104

Q 1 | Page 103

Express the given complex number in the form a + ib: (5i) (- 3/5 i)

Q 2 | Page 103

Express the given complex number in the form a + ibi9 + i19

Q 3 | Page 103

Express the given complex number in the form a + ibi–39

Q 4 | Page 104

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Q 5 | Page 104

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

Q 6 | Page 104

Express the given complex number in the form a + ib: (1/5 + i 2/5) - (4 + i 5/2)

Q 7 | Page 104

Express the given complex number in the form a + ib : [(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)

Q 8 | Page 104

Express the given complex number in the form a + ib:  (1 – i)4

Q 9 | Page 104

Express the given complex number in the form a + ib: (1/3 + 3i)^3

Q 10 | Page 104

Express the given complex number in the form a + ib: (-2 - 1/3 i)^3

Q 11 | Page 104

Find the multiplicative inverse of the complex number 4 – 3i

Q 12 | Page 104

Find the multiplicative inverse of the complex number sqrt5 + 3i

Q 13 | Page 104

Find the multiplicative inverse of the complex number –i

Q 14 | Page 104

Express the following expression in the form of a + ib.

((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))

#### Page 108

Q 1 | Page 108

Find the modulus and the argument of the complex number  z = – 1 – isqrt3

Q 2 | Page 108

Find the modulus and the argument of the complex number z =- sqrt3 + i

Q 3 | Page 108

Convert the given complex number in polar form: 1 – i

Q 4 | Page 108

Convert the given complex number in polar form: – 1 + i

Q 5 | Page 108

Convert the given complex number in polar form: – 1 – i

Q 6 | Page 108

Convert the given complex number in polar form: –3

Q 7 | Page 108

Convert the given complex number in polar form sqrt3 + i

Q 8 | Page 108

Convert the given complex number in polar form: i

#### Page 109

Q 1 | Page 109

Solve the equation x2 + 3 = 0

Q 2 | Page 109

Solve the equation 2x2 + x + 1 = 0

Q 3 | Page 109

Solve the equation x2 + 3x + 9 = 0

Q 4 | Page 109

Solve the equation –x2 + x – 2 = 0

Q 5 | Page 109

Solve the equation x2 + 3x + 5 = 0

Q 5.3 | Page 109

Solve the equation x^2 + x + 1/sqrt2 = 0

Q 6 | Page 109

Solve the equation x2 – x + 2 = 0

Q 7 | Page 109

Solve the equation  sqrt2x^2 + x + sqrt2 = 0

Q 8 | Page 109

Solve the equation  sqrt3 x^2 - sqrt2x + 3sqrt3 = 0

Q 10 | Page 109

Solve the equation  x^2 + x/sqrt2 + 1 = 0

#### Pages 112 - 113

Q 1 | Page 112

Evaluate : [i^18 + (1/i)^25]^3

Q 2 | Page 112

For any two complex numbers z1 and z2, prove that Re (z1z2) = Re zRe z2 – Im z1 Im z2

Q 3 | Page 112

Reduce  (1/(1-4i) - 2/(1+i))((3-4i)/(5+i)) to the standard form.

Q 4 | Page 112

If x – iy = sqrt((a-ib)/(c - id)) prove that (x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)

Q 5.1 | Page 112

Convert the following in the polar form:

(1+7i)/(2-i)^2

Q 5.2 | Page 112

Convert the following in the polar form:

(1+3i)/(1-2i)

Q 6 | Page 112

Solve the equation 3x^2 - 4x + 20/3 = 0

Q 7 | Page 112

Solve the equation   x^2 -2x + 3/2 = 0

Q 7 | Page 112

Solve the equation   x^2 -2x + 3/2 = 0

Q 8 | Page 112

Solve the equation 27x2 – 10+ 1 = 0

Q 9 | Page 113

Solve the equation 21x2 – 28+ 10 = 0

Q 10 | Page 113

If z1 = 2 – i,  z2 = 1 + i, find |(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|

Q 11 | Page 113

If a + ib  = (x + i)^2/(2x^2 + 1) prove that a2 + b2 = (x^2 + 1)^2/(2x + 1)^2

Q 12.1 | Page 113

Let z1 = 2 – i, z2 = –2 + i. Find Re((z_1z_2)/barz_1)

Q 12.2 | Page 113

Let z1 = 2 – i, z2 = –2 + i. Find Im(1/(z_1barz_1))

Q 13 | Page 113

Find the modulus and argument of the complex number (1 + 2i)/(1-3i)

Q 14 | Page 113

Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

Q 15 | Page 113

Find the modulus  of  (1+i)/(1-i) - (1-i)/(1+i)

Q 16 | Page 113

If (x + iy)3 = u + iv, then show that u/x + v/y  =4(x^2 - y^2)

Q 17 | Page 113

If α and β are different complex numbers with |β| = 1, then find |(beta - alpha)/(1-baralphabeta)|

Q 18 | Page 113

Find the number of non-zero integral solutions of the equation |1-i|^x  = 2^x.

Q 19 | Page 113

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.

Q 20 | Page 113

if ((1+i)/(1-i))^m =   1, then find the least positive integral value of m.

## NCERT solutions for Class 11 Mathematics chapter 5 - Complex Numbers and Quadratic Equations

NCERT solutions for Class 11 Mathematics chapter 5 (Complex Numbers and Quadratic Equations) include all questions with solution and detail explanation from Mathematics Textbook for Class 11. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has created the CBSE Mathematics Textbook for Class 11 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics chapter 5 Complex Numbers and Quadratic Equations are Need for Complex Numbers, Algebraic Properties of Complex Numbers, Argand Plane and Polar Representation, Quadratic Equations, Square Root of a Complex Number, Algebra of Complex Numbers, Algebra of Complex Numbers - Equality, Complex Numbers, The Modulus and the Conjugate of a Complex Number.

Using NCERT solutions for Class 11 Mathematics by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

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