Q2 of 202 Page 171

Simplify each of the following and express it in the form (a + ib) :
(2 + i)^–2

Given: (2 + i)^-2

Above equation can be re – written as

Now, rationalizing

[∵ (a – b)² = a² + b² – 2ab]

[∵i² = -1]

…(i)

Now, we know that,

(a + b)(a – b) = (a² – b²)

So, eq. (i) become

Simplify each of the following and express it in the form (a + ib) :

(4 – 3i)^–1

Simplify each of the following and express it in the form (a + ib) :

(1 + 2i)^–3

Simplify each of the following and express it in the form (a + ib) :

(1 + i)³ – (1 – i)³

Simplify each of the following and express it in the form (a + ib) :(2 + i)–2