Question

Вычислите а) -4+3i/-4-3i - -4-3i/-4+3i комплексные числа

Answer 1

Решение
а) -4+3i/-4-3i - -4-3i/-4+3i
(-4+3i)/(-4-3i) = [(- 4 + 3i)*(-4 + 3i)]/[(- 4 - 3i)*(- 4 + 3i)] =
= - (16 - 24i + 9i²) / [(4 + 3i)*(- 4 + 3i)] = - (16 - 24i - 9) / [(3i)² - 4²] =
= - (7 - 24i) / (- 9 - 16) = (7 - 24i) / 25
(- 4 - 3i) / (- 4 + 3i) =  [(- 4 - 3i)*(- 4 - 3i)] / [(- 4 + 3i)* (- 4 - 3i)] = 
(16 + 24i + 9i²) / ((-4)² - 9i²) = (7 + 24i) / 25
 (7 - 24i) / 25 - (7 + 24i) / 25 = (7 - 24i - 7 - 24i) / 25 = - 48i / 25