Multiply the numerator and denominator by the conjugate of i + 1 to get a difference of squares in the denominator:
(2i - 5) / (i + 1) × (-i + 1) / (-i + 1)
((2i - 5) (-i + 1)) / (-i ² - i + i + 1²)
((2i - 5) (-i + 1)) / (-(-1) + 1)
((2i - 5) (-i + 1)) / 2
Expand the numerator:
(2i - 5) (-i + 1) = -2i ² + 5i + 2i - 5 = -3 + 7i
Then we end up with
(2i - 5) / (i + 1) = (-3 + 7i )/2
