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Simplifying (-4 + -3i)(4 + 8i) = 0 Multiply (-4 + -3i) * (4 + 8i) (-4(4 + 8i) + -3i * (4 + 8i)) = 0 ((4 * -4 + 8i * -4) + -3i * (4 + 8i)) = 0 ((-16 + -32i) + -3i * (4 + 8i)) = 0 (-16 + -32i + (4 * -3i + 8i * -3i)) = 0 (-16 + -32i + (-12i + -24i2)) = 0 Combine like terms: -32i + -12i = -44i (-16 + -44i + -24i2) = 0 Solving -16 + -44i + -24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-4'. -4(4 + 11i + 6i2) = 0 Factor a trinomial. -4((4 + 3i)(1 + 2i)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333Subproblem 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 = {-1.333333333, -0.5}
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