Question

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

Answer 1

plz check and let me know whether its correct or not

Answer 2

Let me help you with this question.
Here we have to simplify (4 - 3 i)⁻¹
Solution:
(4 - 3 i)⁻¹ = 1 / (4 - 3 i)
Rationalize the above expression, we get:
(4 - 3 i)⁻¹ = [1 / (4 - 3 i) ] x [ (4 + 3 i) / (4 + 3 i) ]
(4 - 3 i)⁻¹ =  (4 + 3 i) / (4 - 3 i).(4 + 3 i)
(4 - 3 i)⁻¹ = (4 + 3 i) / [ (4) (4) - (3) (3) (i) (i) ]
(4 - 3 i)⁻¹ =  (4 + 3 i) / [ 16 - (9).(i)² ]
(4 - 3 i)⁻¹ = (4 + 3 i) / [ (16 - (9).(-1) ]   (∵ i² = -1)
(4 - 3 i)⁻¹ = (4 + 3 i) / (16 + 9)
(4 - 3 i)⁻¹ = (4 + 3 i) / 25
(4 - 3 i)⁻¹ = (4 / 25) + i (3 / 25)
which is the required answer in the form of (a + i b).
Hope it helps you. Thanks.