Final answer:
To divide 8 by 7-5i, multiply by the complex conjugate of the denominator, simplify, and then express the result in a+bi form, which is 28/37 + 20i/37.
Step-by-step explanation:
To divide 8 by 7-5i, we must multiply the numerator and the denominator by the complex conjugate of the denominator to eliminate the imaginary number in the denominator. The complex conjugate of 7-5i is 7+5i. Therefore, the expression becomes:
(8 / (7-5i)) * ((7+5i) / (7+5i)) = (8*(7+5i)) / ((7-5i)*(7+5i))
Next, we multiply the numerators and the denominators to get:
(56 + 40i) / (49 + 35i - 35i - 25i^2)
Since i^2 = -1, the denominator simplifies to 49 + 25, which gives us 74. Now divide the real and imaginary parts of the numerator by the denominator:
(56/74) + (40i/74) = (28/37) + (20i/37)
Therefore, the answer in the form of a+bi is 28/37 + 20i/37.