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

Question

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

Philoid · Accepted Answer

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