Express the following expression in the form a + ib :
(3 + i√5) (3 - i√5)/[(√3 + √2 i)-(√3 - i√2)]

Solution:

The given complex number is,

(3 + i√5) (3 - i√5)/[(√3 + i√2) (√3 - i√2)]

= (3)² - (i√5)²/ [√3 + i√ 2 √3 + i√ 2] [∵ Using algebraic identity (a + b)(a - b) = a² - b^2].

= (9 - 5i²)/2 i√ 2

= 9 - 5(- 1) / 2 i√ 2  [∵ i² = - 1]

= (9 + 5) / 2i√ 2

= 14/2i√ 2x i/i

= 7i/√2i²

= 7i/√2 (- 1) [∵ i² = - 1]

= - 7i/√2 x √2/√2

= - 7i√2/2

= 0 + i (- 7√2i/2)

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NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.1 Question 14

Express the following expression in the form a + ib : (3 + i√5) (3 - i√5)/[(√3 + √2 i)-(√3 - i√2)]

Summary:

A complex number is given. We have expressed the given complex number in the standard form to be 0 + i (- 7√2i/2).