Question

Write (2 – i)4 in simplest a + bi form.

Answer 1

8 - 4i

Explanation:

(2- i)4

= (2 × 4 - 4 × i)

= 8 - 4i

Answer 2

Answer : 21 - 20i

Explanation:

`{(2 - i)}^(4) = (2 - i) {}^(2) (2 - i) {}^(2) \\ \\ = (4 - 2i - {i}^(2) )(4 - 2i - {i}^(2) )`

remember i² is -1 :

`= (4 - 2i - ( - 1))(4 - 2i - ( - 1)) \\ = (5 - 2i)(5 - 2i) \\ \\ = (25 - 20i + 4 {i}^(2) ) \\ = (25 - 20i + 4( - 1)) \\ = (25 - 20i - 4) \\ = 21 - 20i`