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Simplifying (7 + i)(6 + -9i) = 0 Multiply (7 + i) * (6 + -9i) (7(6 + -9i) + i(6 + -9i)) = 0 ((6 * 7 + -9i * 7) + i(6 + -9i)) = 0 ((42 + -63i) + i(6 + -9i)) = 0 (42 + -63i + (6 * i + -9i * i)) = 0 (42 + -63i + (6i + -9i2)) = 0 Combine like terms: -63i + 6i = -57i (42 + -57i + -9i2) = 0 Solving 42 + -57i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -19i + -3i2) = 0 Factor a trinomial. 3((2 + -3i)(7 + i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 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 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7Solution
i = {0.6666666667, -7}
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