Chapter 5 – Complex Numbers and Quadratic Equations (Ex – 5.1)

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.

Question 1.
(5i)(−3/5i)

Solution.
(5i)(−3/5i)
= -3i² = -3(-1)                    [∵ i² = -1]
= 3
= 3 + 0i

Question 2.
i⁹+ i¹⁹

Solution.

Question 3.
i^-39

Solution.

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.

Question 5.
(1 – i) – (- 1 +i6)

Solution.
(1 – i) – (-1 + i6) = 1 – i + 1 – 6i
= (1 +1) – i(1 + 6)
= 2 – 7i

Question 6.
(1/5+i2/5)−(4+i5/2)

Solution.

Question 7.
[(1/3+i7/3)+(4+i1/3)]−(−4/3+i)

Solution.

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

Question 9.
(1/3+3i)³

Solution.

Question 10.
(−2−1/3i)3

Solution.

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

Question 11.
4 – 3i

Solution.

Ex 5.1 Class 11 Maths Question 12.
√5+3i
Solution.

Question 13.
-i

Solution.

Question 14.

Solution.