Q2 of 202 Page 171

Simplify each of the following and express it in the form (a + ib) :
(4 – 3i)^–1

Given: (4 – 3i)^-1

We can re- write the above equation as

Now, rationalizing

…(i)

Now, we know that,

(a + b)(a – b) = (a² – b²)

So, eq. (i) become

[∵ i² = -1]

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

(–3 + 5i)³

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

(2 + i)^–2

Simplify each of the following and express it in the form (a + ib) :(4 – 3i)–1