Final answer:
To divide complex numbers, use the formula: (a + bi) ÷ (c + di) = (ac + bd) ÷ (c^2 + d^2) + ((bc - ad) ÷ (c^2 + d^2))i. Using this formula, (5 - 7i) ÷ (2 - 5i) equals approximately 1.3448275862068966 - 1.3448275862068966i.
Step-by-step explanation:
To find the quotient of complex numbers, we can use the formula:
(a + bi) ÷ (c + di) = (ac + bd) ÷ (c^2 + d^2) + ((bc - ad) ÷ (c^2 + d^2))i
Using this formula, we can divide (5 - 7i) by (2 - 5i) as follows:
(5 - 7i) ÷ (2 - 5i) = [(5)(2) + (-7)(-5)] ÷ [(2)^2 + (-5)^2] + [(-7)(2) - (5)(5)] ÷ [(2)^2 + (-5)^2]i = (14 + 35) ÷ (4 + 25) + (-14 - 25) ÷ (4 + 25)i = 49 ÷ 29 + (-39) ÷ 29i = 1.3448275862068966 - 1.3448275862068966i.