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galina1969 [7]
3 years ago
10

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

Mathematics
2 answers:
mr_godi [17]3 years ago
3 0

Answer:

<u>Answer</u><u> </u><u>:</u><u> </u><u>2</u><u>1</u><u> </u><u>-</u><u> </u><u>2</u><u>0</u><u>i</u>

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

kirill115 [55]3 years ago
3 0

Answer:

8 - 4i

Step-by-step explanation:

(2- i)4

= (2 × 4 - 4 × i)

= 8 - 4i

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