Question

Комплексные числа. Желательно подробно
Z1= 7-9i
Z2= 4-8i
Z3=11+13i
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.
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1)Z3/Z1 - Z2/Z3
2) (Z1+Z2)*Z3/Z1

Answer 1

1) $\frac{11+13i}{7-9i} -\frac{4-8i}{11+13i} =\frac{(11+13i)(7+9i)}{(7-9i)(7+9i)} -\frac{(4-8i)(11-13i)}{(11+13i)(11-13i)}=\\=\frac{77+91i+99i-117}{49+81}  -\frac{44-88i-52i-104}{121+169} =\\=\frac{-40+190i}{130} -\frac{-60-140i}{290} =\frac{-4+19i}{13} +\frac{6+14i}{29} =\frac{-38+733i}{377}$

2) $\frac{(7-9i+4-8i)(11+13i)}{7-9i} =\frac{(11-17i)(11+13i)(7+9i)}{49+81} =\\=\frac{(121-187i+143i+221)(7+9i)}{130} =\frac{(342-44i)(7+9i)}{130} =\frac{2790+2770i}{130} =\\=\frac{279+277i}{13}$