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Divide the complex numbers. Write the answer in the form a + bi. (30 points)

Prefer work shown as it would be super helpful, thank you.

Divide the complex numbers Write the answer in the form a bi 30 points Prefer work shown as it would be super helpful thank you class=

Respuesta :

LammettHash

We make use of the identity,

a² - b² = (a - b) (a + b)

with a = 5 and b = 7i. Multiply the numerator and denominator by the complex conjugate of 5 + 7i, or 5 - 7i :

(-8 + 3i)/(5 + 7i) = (-8 + 3i)/(5 + 7i) • (5 - 7i)/(5 - 7i)

(-8 + 3i)/(5 + 7i) = (-8 + 3i) (5 - 7i) / (5² - (7i)²)

(-8 + 3i)/(5 + 7i) = (-8 + 3i) (5 - 7i) / (25 - (-49))

(-8 + 3i)/(5 + 7i) = (-8 + 3i) (5 - 7i) / 74

Expand the numerator on the right side:

(-8 + 3i)/(5 + 7i) = ((-8)•5 + 3i•5 + (-8)•(-7i) + 3i•(-7i)) / 74

(-8 + 3i)/(5 + 7i) = (-40 + 15i + 56i - 21i²) / 74

(-8 + 3i)/(5 + 7i) = (-40 + 71i - 21(-1)) / 74

(-8 + 3i)/(5 + 7i) = (-19 + 71i) / 74

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