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LenaVadim1999
@LenaVadim1999
July 2022
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пожалуйста помогите решить алгебраические комплексные числа 1) 5+I/2+i3; 2) 3i^15+(i корень 3)^2/i^9 ОЧЕНЬ НУЖНО
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Verified answer
1) (5 + i)/(2 + 3*i) = (5 + i)(2 - 3*i) / [(2 + 3*i)(2 - 3*i)] =
(10+2*i-5*3*i-i*3*i) / (4-9i^2) = (13 - 12*i)/(4 + 9) = (13 - 12*i)/13 = 1 - 12*i/13
2) 3i^15 + (√3*i)^2/i^9 = 3i^12*i^3 + 3*i^2 / (i^8*i) = 3*1(-i) - 3 / i = -3*i + 3*i = 0
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Answers & Comments
Verified answer
1) (5 + i)/(2 + 3*i) = (5 + i)(2 - 3*i) / [(2 + 3*i)(2 - 3*i)] =(10+2*i-5*3*i-i*3*i) / (4-9i^2) = (13 - 12*i)/(4 + 9) = (13 - 12*i)/13 = 1 - 12*i/13
2) 3i^15 + (√3*i)^2/i^9 = 3i^12*i^3 + 3*i^2 / (i^8*i) = 3*1(-i) - 3 / i = -3*i + 3*i = 0