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@Ведьмавкедах
August 2021
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Помогите решить действия с комплексными числами
(3-5i)^2
и еще деление
2-3i/5+2i
а еще
5-7i/5+7i
и еще
6-7i/i
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Dимасuk
Verified answer
(3 - 5i)² = 9 - 30i + 25i² = 9 - 25 - 30i = -16 - 30i
(2 - 3i)/(5 + 2i) = (2 - 3i)(5 - 2i)/(5 + 2i)(5 - 2i) = (10 - 4i - 15i + 6i²)/(25 - 4i²) =
= (10 - 6 - 19i)/(25 + 4) = (4 - 19i)/29 = 4/29 - 19i/29
(5 - 7i)/(5 + 7i) = (5 - 7i)²/(5 + 7i)(5 - 7i) = (25 - 70i + 49i²)/(25 - 49i²) =
= (-24 - 70i)/74 = -12/37 - 35i/37
(6 - 7i)/i = i(6 - 7i)/i² = (6i - 7i²)/(-1) = (6i + 7)/(-1) = -7 - 6i
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Answers & Comments
Verified answer
(3 - 5i)² = 9 - 30i + 25i² = 9 - 25 - 30i = -16 - 30i(2 - 3i)/(5 + 2i) = (2 - 3i)(5 - 2i)/(5 + 2i)(5 - 2i) = (10 - 4i - 15i + 6i²)/(25 - 4i²) =
= (10 - 6 - 19i)/(25 + 4) = (4 - 19i)/29 = 4/29 - 19i/29
(5 - 7i)/(5 + 7i) = (5 - 7i)²/(5 + 7i)(5 - 7i) = (25 - 70i + 49i²)/(25 - 49i²) =
= (-24 - 70i)/74 = -12/37 - 35i/37
(6 - 7i)/i = i(6 - 7i)/i² = (6i - 7i²)/(-1) = (6i + 7)/(-1) = -7 - 6i