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,
