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Simplifying (2 + 3i)(-4 + 2i) = 0 Multiply (2 + 3i) * (-4 + 2i) (2(-4 + 2i) + 3i * (-4 + 2i)) = 0 ((-4 * 2 + 2i * 2) + 3i * (-4 + 2i)) = 0 ((-8 + 4i) + 3i * (-4 + 2i)) = 0 (-8 + 4i + (-4 * 3i + 2i * 3i)) = 0 (-8 + 4i + (-12i + 6i2)) = 0 Combine like terms: 4i + -12i = -8i (-8 + -8i + 6i2) = 0 Solving -8 + -8i + 6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -4i + 3i2) = 0 Factor a trinomial. 2((-2 + -3i)(2 + -1i)) = 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 '(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 = {-0.6666666667, 2}
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