In This Post we are providing Chapter -5 Complex Numbers and Quadratic Equations NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These Class 11 Complex Numbers and Quadratic Equations solutions can be really helpful in the preparation of Board exams and will provide you with in depth detail of the chapter.
We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths Complex Numbers and Quadratic Equations NCERT Written Solutions will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.
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.
Solution.
= -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.
Solution.
Ex 5.1 Class 11 Maths Question 7.
Solution.
![\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right)](https://s0.wp.com/latex.php?latex=%5Cleft%5B+%5Cleft%28+%5Cfrac+%7B+1+%7D%7B+3+%7D+%2Bi%5Cfrac+%7B+7+%7D%7B+3+%7D+%5Cright%29+%2B%5Cleft%28+4%2Bi%5Cfrac+%7B+1+%7D%7B+3+%7D+%5Cright%29+%5Cright%5D+-%5Cleft%28+-%5Cfrac+%7B+4+%7D%7B+3+%7D+%2Bi+%5Cright%29+&bg=ffffff&fg=000&s=0 "\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right)")
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.
Solution.
Ex 5.1 Class 11 Maths Question 10.
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.
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:
Solution.
We have, 
We hope the NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1, drop a comment below and we will get back to you at the earliest.
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.
Solution.
We have, 
Ex 5.2 Class 11 Maths Question 2.
Solution.
We have, 
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.
Solution.
We have, 
Ex 5.2 Class 11 Maths Question 8.
i
Solution.
We have, z = i, i.e., z = 0 + 1.i
We hope the NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2, drop a comment below and we will get back to you at the earliest.
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
⇒ 
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.
Solution.
We have,
Comparing the given equation with the general form ax2 + bx + c = 0, we get
Ex 5.3 Class 11 Maths Question 8.
Solution.
We have,
Comparing the given equation with the general form ax2 + bx + c = 0, we get
Ex 5.3 Class 11 Maths Question 9.
Solution.
We have,
Comparing the given equation with the general form ax2 + bx + c = 0, we get
Ex 5.3 Class 11 Maths Question 10.
Solution.
We have,
Comparing the given equation with the general form ax2 + bx + c = 0, we get
We hope the NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3, drop a comment below and we will get back to you at the earliest.
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