Question

The division (5+4i)/(6-6i) is performed by multiplying the numerator and denominator by---

Answer 1

To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator.

Step-by-step explanation:

To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of 6-6i is 6+6i. So, we multiply both the numerator and denominator by 6+6i:

(5+4i)/(6-6i) * (6+6i)/(6+6i)

Expanding the expression, we get:

(30+30i+24i+24i^2)/(36-36i+36i-36i^2)

Simplifying further:

(30+54i-24)/(36+36)

(6+54i)/72

Dividing both the real and imaginary parts of the complex number by 72:

6/12 + 54i/72

Reducing the fractions:

1/2 + 3i/4

So, the division (5+4i)/(6-6i) is equal to 1/2 + 3i/4.

Learn more about Dividing Complex Numbers