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Simplifying (2 + 4i)(-6 + -3i) = 0 Multiply (2 + 4i) * (-6 + -3i) (2(-6 + -3i) + 4i * (-6 + -3i)) = 0 ((-6 * 2 + -3i * 2) + 4i * (-6 + -3i)) = 0 ((-12 + -6i) + 4i * (-6 + -3i)) = 0 (-12 + -6i + (-6 * 4i + -3i * 4i)) = 0 (-12 + -6i + (-24i + -12i2)) = 0 Combine like terms: -6i + -24i = -30i (-12 + -30i + -12i2) = 0 Solving -12 + -30i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-6'. -6(2 + 5i + 2i2) = 0 Factor a trinomial. -6((2 + i)(1 + 2i)) = 0 Ignore the factor -6.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 '(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 = -0.5Solution
i = {-2, -0.5}
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