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Chapters
2: Relations and Functions
3: Trigonometric Functions
▶ 4: Complex Numbers and Quadratic Equations
5: Linear Inequalities
6: Permutations and Combinations
7: Binomial Theorem
8: Sequences and Series
9: Straight Lines
10: Conic Sections
11: Introduction to Three Dimensional Geometry
12: Limits and Derivatives
13: Statistics
14: Probability
![NCERT solutions for Mathematics [English] Class 11 chapter 4 - Complex Numbers and Quadratic Equations - Shaalaa.com](/images/mathematics-english-class-11_6:6ab366e2671b448497dd3d3a0e6fed94.jpg "NCERT solutions for Mathematics [English] Class 11 chapter 4 - Complex Numbers and Quadratic Equations")
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Solutions for Chapter 4: Complex Numbers and Quadratic Equations
Below listed, you can find solutions for Chapter 4 of CBSE, Karnataka Board PUC NCERT for Mathematics [English] Class 11.
NCERT solutions for Mathematics [English] Class 11 4 Complex Numbers and Quadratic Equations EXERCISE 4.1 [Pages 82 - 83]
Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`
Express the given complex number in the form a + ib: i9 + i19
Express the given complex number in the form a + ib: i–39
Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)
Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Express the given complex number in the form a + ib:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
Express the given complex number in the form a + ib: (1 – i)4
Express the given complex number in the form a + ib: `(1/3 + 3i)^3`
Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`
Find the multiplicative inverse of the complex number:
4 – 3i
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Find the multiplicative inverse of the complex number.
–i
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
NCERT solutions for Mathematics [English] Class 11 4 Complex Numbers and Quadratic Equations Miscellaneous Exercise [Pages 85 - 86]
Evaluate: `[i^18 + (1/i)^25]^3`
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2 – Imz1 Imz2
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
If z1 = 2 – i, z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.
Find the modulus of \[\frac{1 + i}{1 - i} - \frac{1 - i}{1 + i}\].
If (x + iy)3 = u + iv, then show that `u/x + v/y =4(x^2 - y^2)`
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Solutions for 4: Complex Numbers and Quadratic Equations
NCERT solutions for Mathematics [English] Class 11 chapter 4 - Complex Numbers and Quadratic Equations
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Concepts covered in Mathematics [English] Class 11 chapter 4 Complex Numbers and Quadratic Equations are Argand Plane and Polar Representation, Quadratic Equations, Algebra of Complex Numbers - Equality, Algebraic Properties of Complex Numbers, Need for Complex Numbers, Square Root of a Complex Number, Algebraic Operations of Complex Numbers, The Modulus and the Conjugate of a Complex Number, Concept of Complex Numbers, Argand Plane and Polar Representation, Quadratic Equations, Algebra of Complex Numbers - Equality, Algebraic Properties of Complex Numbers, Need for Complex Numbers, Square Root of a Complex Number, Algebraic Operations of Complex Numbers, The Modulus and the Conjugate of a Complex Number, Concept of Complex Numbers.
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