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Simplifying 0 = (8 + -4i)(3 + -2i) Multiply (8 + -4i) * (3 + -2i) 0 = (8(3 + -2i) + -4i * (3 + -2i)) 0 = ((3 * 8 + -2i * 8) + -4i * (3 + -2i)) 0 = ((24 + -16i) + -4i * (3 + -2i)) 0 = (24 + -16i + (3 * -4i + -2i * -4i)) 0 = (24 + -16i + (-12i + 8i2)) Combine like terms: -16i + -12i = -28i 0 = (24 + -28i + 8i2) Solving 0 = 24 + -28i + 8i2 Solving for variable 'i'. Combine like terms: 0 + -24 = -24 -24 + 28i + -8i2 = 24 + -28i + 8i2 + -24 + 28i + -8i2 Reorder the terms: -24 + 28i + -8i2 = 24 + -24 + -28i + 28i + 8i2 + -8i2 Combine like terms: 24 + -24 = 0 -24 + 28i + -8i2 = 0 + -28i + 28i + 8i2 + -8i2 -24 + 28i + -8i2 = -28i + 28i + 8i2 + -8i2 Combine like terms: -28i + 28i = 0 -24 + 28i + -8i2 = 0 + 8i2 + -8i2 -24 + 28i + -8i2 = 8i2 + -8i2 Combine like terms: 8i2 + -8i2 = 0 -24 + 28i + -8i2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 7i + -2i2) = 0 Factor a trinomial. 4((-2 + i)(3 + -2i)) = 0 Ignore the factor 4.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 '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {2, 1.5}
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