Evaluate the expression (-9 - 10i) / (4 + 7i), and write your answer in the form a + bi. a = ____ and b = ____
Evaluate the expression (-9 - 10i) / (4 + 7i), and write your answer in the form a + bi.
a = ____ and b = ____
a = ____ and b = ____
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info@snapandsolve.comTo evaluate the expression (-9 - 10i) / (4 + 7i), we multiply the numerator and the denominator by the conjugate of the denominator:
(-9 - 10i)(4 - 7i) / (4 + 7i)(4 - 7i)
(4 + 7i)(4 - 7i) = 4^2 - (7i)^2 = 16 + 49 = 65
(-9 - 10i)(4 - 7i) = (-9)(4) + (-9)(-7i) + (-10i)(4) + (-10i)(-7i)
= -36 + 63i - 40i + 70i^2
= -36 + 23i - 70
= -106 + 23i
a = -106 / 65 = -1.63
b = 23 / 65 = 0.35
Thus, the answer is a = -1.63 and b = 0.35.
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