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Simplifying (2 + -4i)(4 + -6i) = 0 Multiply (2 + -4i) * (4 + -6i) (2(4 + -6i) + -4i * (4 + -6i)) = 0 ((4 * 2 + -6i * 2) + -4i * (4 + -6i)) = 0 ((8 + -12i) + -4i * (4 + -6i)) = 0 (8 + -12i + (4 * -4i + -6i * -4i)) = 0 (8 + -12i + (-16i + 24i2)) = 0 Combine like terms: -12i + -16i = -28i (8 + -28i + 24i2) = 0 Solving 8 + -28i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -7i + 6i2) = 0 Factor a trinomial. 4((1 + -2i)(2 + -3i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Subproblem 2
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 = 0.6666666667Solution
i = {0.5, 0.6666666667}
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