Answer:
Explanation:
To find the product or quotient of the expression (5 - 4i)/(5 + 4i) using trigonometric form, we can multiply the numerator and denominator by the conjugate of the denominator, which is (5 - 4i):
((5 - 4i)/(5 + 4i)) * ((5 - 4i)/(5 - 4i))
Expanding the numerator and denominator:
((25 - 20i - 20i + 16i^2)/(25 - 20i + 20i - 16i^2))
Simplifying and using the fact that i^2 = -1:
((25 - 20i - 20i - 16*(-1))/(25 - (-16)))
((25 - 20i - 20i + 16)/(25 + 16))
(41 - 40i)/(41)
Dividing each term by 41:
41/41 - (40i/41)
1 - (40/41)i
Therefore, the quotient (5 - 4i)/(5 + 4i) in the form a+bi is 1 - (40/41)i.