NCERT Solutions | Class 11 Maths Chapter 5 | Quadratic equations and complex numbers

CBSE Solutions | Maths Class 11

Check the below NCERT Solutions for Class 11 Maths Chapter 5 Quadratic equations and complex numbers Pdf free download. NCERT Solutions Class 11 Maths  were prepared based on the latest exam pattern. We have Provided Quadratic equations and complex numbers Class 11 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 11 Maths

Book: National Council of Educational Research and Training (NCERT) Central Board of Secondary Education (CBSE) 11th Maths 5 Quadratic equations and complex numbers English

Quadratic equations and complex numbers | Class 11 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 11 Maths Chapter 5 Quadratic equations and complex numbers to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.

Ex 5.1 Class 11 Maths Question 1.
$$\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right)$$
Solution.
$$\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right)$$
= -3i2 = -3(-1) [∵ i2 = -1]
= 3 = 3 + 0i

Ex 5.1 Class 11 Maths Question 2.
i9+ i19
Solution.

Ex 5.1 Class 11 Maths Question 3.
i-39
Solution.

Ex 5.1 Class 11 Maths Question 4.
3(7 + i7) + i(7 + i7)
Solution.
3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i2
= 21 + (21 + 7)i + (-1)7 = 21 – 7 + 28i
= 14 + 28i.

Ex 5.1 Class 11 Maths Question 5.
(1 – i) – (- 1 +i6)
Solution.
(1 – i) – (-1 + i6) = 1 – i + 1 – 6i
= (1 +1) – i(1 + 6)
= 2 – 7i

Ex 5.1 Class 11 Maths Question 6.
$$\left( \frac { 1 }{ 5 } +i\frac { 2 }{ 5 } \right) -\left( 4+i\frac { 5 }{ 2 } \right)$$
Solution.

Ex 5.1 Class 11 Maths Question 7.
$$\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right)$$
Solution.

Ex 5.1 Class 11 Maths Question 8.
(1 -i)4
Solution.
(1 -i)4 = [(1 – i)2]2 = [1 – 2i + i2]2
= [1 – 2i + (-1)]2
= (-2i)2 = 4i2 = 4(-1) = – 4
= – 4 + 0i

Ex 5.1 Class 11 Maths Question 9.
$${ \left( \frac { 1 }{ 3 } +3i \right) }^{ 3 }$$
Solution.

Ex 5.1 Class 11 Maths Question 10.
$${ \left( -2-\frac { 1 }{ 3 } i \right) }^{ 3 }$$
Solution.

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.

Ex 5.1 Class 11 Maths Question 11.
4 – 3i
Solution.

Ex 5.1 Class 11 Maths Question 12.
$$\sqrt { 5 } +3i$$
Solution.

Ex 5.1 Class 11 Maths Question 13.
-i
Solution.

Ex 5.1 Class 11 Maths Question 14.
Express the following expression in the form of a + ib:
$$\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }$$
Solution.
We have, $$\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }$$

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.

Ex 5.2 Class 11 Maths Question 1.
$$z=-1-i\sqrt { 3 }$$
Solution.
We have, $$z=-1-i\sqrt { 3 }$$

Ex 5.2 Class 11 Maths Question 2.
$$z=-\sqrt { 3 } +i$$
Solution.
We have, $$z=-\sqrt { 3 } +i$$

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:

Ex 5.2 Class 11 Maths Question 3.
1 – i
Solution.
We have, z = 1 – i

Ex 5.2 Class 11 Maths Question 4.
-1 + i
Solution.
We have, z = -1 + i

Ex 5.2 Class 11 Maths Question 5.
-1 – i
Solution.
We have, z = -1 – i

Ex 5.2 Class 11 Maths Question 6.
-3
Solution.
We have, z = -3, i.e., z = -3 + 0i

Ex 5.2 Class 11 Maths Question 7.
$$\sqrt { 3 } +i$$
Solution.
We have, $$z=\sqrt { 3 } +i$$

Ex 5.2 Class 11 Maths Question 8.
i
Solution.
We have, z = i, i.e., z = 0 + 1.i

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Solve each of the following equations:

Ex 5.3 Class 11 Maths Question 1.
x2 + 3 = 0
Solution.
We have, x2 + 3 = 0 ⇒ x2 = -3
⇒ $$x=\pm \sqrt { -3 }$$ ⇒ x = $$\pm \sqrt { 3 } i$$

Ex 5.3 Class 11 Maths Question 2.
2x2 + x + 1 = 0
Solution.
We have, 2x2 + x + 1 = 0
Comparing the given equation with the general form ax2 + bx + c = 0, we get

Ex 5.3 Class 11 Maths Question 3.
x2 + 3x + 9 = 0
Solution.
We have, x2 + 3x + 9 = 0
Comparing the given equation with the general form ax2 + bx + c = 0,we get a = 1, b = 3, c = 9

Ex 5.3 Class 11 Maths Question 4.
-x2 + x – 2 = 0
Solution.
We have, -x2 + x – 2 = 0
Comparing the given equation with the general form ax2 + bx + c = 0,we get
a = 1, b = 1, c = -2

Ex 5.3 Class 11 Maths Question 5.
x2 + 3x + 5 = 0
Solution.
We have, x2 + 3x + 5 = 0
Comparing the given equation with the general form ax2 + bx + c = 0, we get a = 1, b = 3, c = 5.

Ex 5.3 Class 11 Maths Question 6.
x2 – x + 2 = 0
Solution.
We have, x2 – x + 2 = 0
Comparing the given equation with the general form ax2 + bx + c = 0, we get a = 1, b = -1, c = 2.

Ex 5.3 Class 11 Maths Question 7.
$$\sqrt { 2 } { x }^{ 2 }+x+\sqrt { 2 } =0$$
Solution.
We have, $$\sqrt { 2 } { x }^{ 2 }+x+\sqrt { 2 } =0$$
Comparing the given equation with the general form ax2 + bx + c = 0, we get

Ex 5.3 Class 11 Maths Question 8.
$$\sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+3\sqrt { 3 } =0$$
Solution.
We have, $$\sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+3\sqrt { 3 } =0$$
Comparing the given equation with the general form ax2 + bx + c = 0, we get

Ex 5.3 Class 11 Maths Question 9.
$${ x }^{ 2 }+x+\frac { 1 }{ \sqrt { 2 } } =0$$
Solution.
We have, $${ x }^{ 2 }+x+\frac { 1 }{ \sqrt { 2 } } =0$$
Comparing the given equation with the general form ax2 + bx + c = 0, we get

Ex 5.3 Class 11 Maths Question 10.
$${ x }^{ 2 }+\frac { x }{ \sqrt { 2 } } +1=0$$
Solution.
We have, $${ x }^{ 2 }+\frac { x }{ \sqrt { 2 } } +1=0$$
Comparing the given equation with the general form ax2 + bx + c = 0, we get