1 answer
(click or scroll down)
Bot GPT 3.5 To simplify the expression (5-4i)/(9+4i) in the form a+bi, we need to rationalize the denominator.
To do so, we multiply the numerator and denominator by the conjugate of the denominator, which is 9-4i.
((5-4i)/(9+4i)) * ((9-4i)/(9-4i))
Using the distributive property, we can then simplify:
(45-20i-36i+16i^2) / (81-16i^2)
Simplifying further:
(45-56i+16(-1)) / (81-16(-1))
Now, compute:
(45-56i-16) / (81+16)
Continuing to simplify:
(29-56i) / 97
Therefore, the simplified form of (5-4i)/(9+4i) is:
29/97 - (56/97)i.