Question

Express (2i - 5) / (i + 1) in its simplest form in terms of i.

Answer 1

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