Rationalize the denominator: 7 + 5i/-7j

Answer 1

To rationalize the denominator, we want to eliminate the complex number in the denominator, which is -7j. To do this, we can multiply both the numerator and denominator by the conjugate of the denominator, which is 7j.

(7 + 5i)(7j) / (-7j)(7j)

Expanding the numerator, we get:

49j + 35ij

And expanding the denominator, we get:

49j^2

Since j is defined as the imaginary unit, j^2 can be replaced with -1:

49(-1)

Simplifying, we have:

-49

Therefore, the rationalized form of the fraction is:

(49j + 35ij) / (-49)