NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations Ex 4.1 are the part of NCERT Solutions for Class 11 Maths. In this post, you will find the NCERT Solutions for Class 11 Maths chapter 4 Complex Numbers and Quadratic Equations Ex 4.1.
NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations Ex 4.1
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.
Ex 4.1 Class 11 Maths Question 1.
(5i)(−3i/5)
Solution.
(5i)(−i3/5)
= -3i2 = -3(-1) [∵ i2 = -1]
= 3 = 3 + 0i
Ex 4.1 Class 11 Maths Question 2.
i9 + i19
Solution.
i9 + i19 = (i2)4.i + (i2)9.i = (-1)4.i + (-1)9.i
= i + (-1)i = i – i = 0 = 0 + 0i
Ex 4.1 Class 11 Maths Question 3.
i-39
Solution.
Ex 4.1 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 4.1 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 4.1 Class 11 Maths Question 6.
Solution.
Ex 4.1 Class 11 Maths Question 7.
Solution.
Ex 4.1 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 4.1 Class 11 Maths Question 9.
(1/3 + 3i)3
Solution.
Ex 4.1 Class 11 Maths Question 10.
(−2 – 1/3 i)3
Solution.
Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.
Ex 4.1 Class 11 Maths Question 11.
4 – 3i
Solution.
Ex 4.1 Class 11 Maths Question 12.
√5 + 3i
Solution.
Ex 4.1 Class 11 Maths Question 13.
-i
Solution.
Ex 4.1 Class 11 Maths Question 14.
Express the following expression in the form of a + ib:
Solution.
We have,
