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Find the product or quotient, using trigonometric form. Write the answer in the form a+bi. 5-4i/5+4i

User Rctneil
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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.

User Pieter Maes
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