Express each of the complex number given in the Exercises 1 to 10 in the form a + ib :
i⁹ + i¹⁹

Solution:

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers.

The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).  Also, ib is called an imaginary number.

The given complex number is,

i⁹ + i¹⁹ = i^{4 x 2 + 1} + i^{4 x 4 + 3}

= (i⁴ )² x i + (i⁴)⁴ x i³

= 1 x i + 1 x (- i) [∵ i⁴= 1, i³ = - i]

= i + (- i)

= 0

= 0 + i0

NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.1 Question 2

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib : i⁹ + i¹⁹

Summary:

A complex number is given. We have expressed the given complex number in the standard form to be 0 + i0