5-4i/9+4i

Answer 1

To simplify the expression (5-4i)/(9+4i), we will multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of 9+4i is 9-4i.

So, multiplying the numerator and denominator by the conjugate, we get:

((5-4i)*(9-4i))/((9+4i)*(9-4i))

Expanding the numerators and denominators, we have:

(45-20i-36i+16i²)/(81-16i²)

Simplifying further, we have:

(45-56i+16i²)/(81-16i²)

Now, we can substitute the value of i², which is -1:

(45-56i+16(-1))/(81-16(-1))

Simplifying, we get:

(45-56i-16)/(81+16)

Combining like terms, we have:

(29-56i)/97