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Simplifying (7 + -6i)(8 + -4i) = 0 Multiply (7 + -6i) * (8 + -4i) (7(8 + -4i) + -6i * (8 + -4i)) = 0 ((8 * 7 + -4i * 7) + -6i * (8 + -4i)) = 0 ((56 + -28i) + -6i * (8 + -4i)) = 0 (56 + -28i + (8 * -6i + -4i * -6i)) = 0 (56 + -28i + (-48i + 24i2)) = 0 Combine like terms: -28i + -48i = -76i (56 + -76i + 24i2) = 0 Solving 56 + -76i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(14 + -19i + 6i2) = 0 Factor a trinomial. 4((7 + -6i)(2 + -1i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -6i)' equal to zero and attempt to solve: Simplifying 7 + -6i = 0 Solving 7 + -6i = 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 + -6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6i = 0 + -7 -6i = 0 + -7 Combine like terms: 0 + -7 = -7 -6i = -7 Divide each side by '-6'. i = 1.166666667 Simplifying i = 1.166666667Subproblem 2
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Solution
i = {1.166666667, 2}
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