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Simplifying (8 + 4i)(-6 + -7i) = 0 Multiply (8 + 4i) * (-6 + -7i) (8(-6 + -7i) + 4i * (-6 + -7i)) = 0 ((-6 * 8 + -7i * 8) + 4i * (-6 + -7i)) = 0 ((-48 + -56i) + 4i * (-6 + -7i)) = 0 (-48 + -56i + (-6 * 4i + -7i * 4i)) = 0 (-48 + -56i + (-24i + -28i2)) = 0 Combine like terms: -56i + -24i = -80i (-48 + -80i + -28i2) = 0 Solving -48 + -80i + -28i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-4'. -4(12 + 20i + 7i2) = 0 Factor a trinomial. -4((2 + i)(6 + 7i)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Subproblem 2
Set the factor '(6 + 7i)' equal to zero and attempt to solve: Simplifying 6 + 7i = 0 Solving 6 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7i = 0 + -6 7i = 0 + -6 Combine like terms: 0 + -6 = -6 7i = -6 Divide each side by '7'. i = -0.8571428571 Simplifying i = -0.8571428571Solution
i = {-2, -0.8571428571}
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