rationalize the denominator

Question

7 + 5i / -7i

Answer 1

To rationalize the denominator in this expression, multiply both the numerator and the denominator by the conjugate of the denominator.

The conjugate of -7i is 7i, so we multiply both the numerator and denominator by 7i:

(7 + 5i) / (-7i) * (7i / 7i)
= (7 + 5i)(7i) / (-7i)(7i)
= 49i + 35i^2 / -49i^2

Remember that i^2 = -1, so we can simplify this further:
= 49i + 35(-1) / -49(-1)
= 49i - 35 / 49

So, the rationalized form of the expression is (49i - 35) / 49.