simplify in the form of a+bi

9-4i/9+8i

1 answer

To simplify the expression (9-4i)/(9+8i) in the form a+bi, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (9-8i). This will eliminate the imaginary term in the denominator.

(9-4i)(9-8i) / (9+8i)(9-8i)

Expanding the numerator and denominator:

(81-72i-36i+32i^2) / (81-64i^2)

Simplifying the numerator:

(81-108i+32(-1)) / (81-64(-1))

(81-108i-32) / (81+64)

(-50-108i) / 145

Dividing both the real and imaginary parts by 145:

-50/145 - (108/145)i

Therefore, the simplified form of (9-4i)/(9+8i) is -10/29 - (216/435)i.