Express each of the complex number given in the Exercises 1 to 10 in the form a + ib :
(1/3 + 3i)³

Solution:

The given complex number is,

(1/3 + 3i)³

= (1/3)³ + (3i)³ + 3(1/3) (3i) (1/3 + 3i)  [∵ (a + b)³ = a³ + b³ + 3ab (a + b) ]

= 1/27 + 27i³ + (3i) (1/3 + 3i)

= 1/27 + 27(- i) + i + 9i² [∵ i³ = - i]

= 1/27 - 27i + i - 9 [∵ i² = - 1]

= (1/27 - 9) - 26i

= - 242/27 - i26

NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.1 Question 9

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib : (1/3 + 3i)³

Summary:

A complex number is given. We have expressed the given complex number in the standard form to be - 242/27 - i26