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Simplifying (8 + -3i)(4 + 2i) = 0 Multiply (8 + -3i) * (4 + 2i) (8(4 + 2i) + -3i * (4 + 2i)) = 0 ((4 * 8 + 2i * 8) + -3i * (4 + 2i)) = 0 ((32 + 16i) + -3i * (4 + 2i)) = 0 (32 + 16i + (4 * -3i + 2i * -3i)) = 0 (32 + 16i + (-12i + -6i2)) = 0 Combine like terms: 16i + -12i = 4i (32 + 4i + -6i2) = 0 Solving 32 + 4i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 2i + -3i2) = 0 Factor a trinomial. 2((8 + -3i)(2 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -3i)' equal to zero and attempt to solve: Simplifying 8 + -3i = 0 Solving 8 + -3i = 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 + -3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3i = 0 + -8 -3i = 0 + -8 Combine like terms: 0 + -8 = -8 -3i = -8 Divide each side by '-3'. i = 2.666666667 Simplifying i = 2.666666667Subproblem 2
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 = -2Solution
i = {2.666666667, -2}
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