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Simplifying (-8 + 7i)(-4 + 6i) = 0 Multiply (-8 + 7i) * (-4 + 6i) (-8(-4 + 6i) + 7i * (-4 + 6i)) = 0 ((-4 * -8 + 6i * -8) + 7i * (-4 + 6i)) = 0 ((32 + -48i) + 7i * (-4 + 6i)) = 0 (32 + -48i + (-4 * 7i + 6i * 7i)) = 0 (32 + -48i + (-28i + 42i2)) = 0 Combine like terms: -48i + -28i = -76i (32 + -76i + 42i2) = 0 Solving 32 + -76i + 42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -38i + 21i2) = 0 Factor a trinomial. 2((2 + -3i)(8 + -7i)) = 0 Ignore the factor 2.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 '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Solution
i = {0.6666666667, 1.142857143}
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