Question

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

Answer 1

Answer:

Answer : 21 - 20i

Step-by-step explanation:

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

remember i² is -1 :

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

Answer 2

Answer:

8 - 4i

Step-by-step explanation:

(2- i)4

= (2 × 4 - 4 × i)

= 8 - 4i