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Simplifying (-4 + -4i)(2 + 4i) = 0 Multiply (-4 + -4i) * (2 + 4i) (-4(2 + 4i) + -4i * (2 + 4i)) = 0 ((2 * -4 + 4i * -4) + -4i * (2 + 4i)) = 0 ((-8 + -16i) + -4i * (2 + 4i)) = 0 (-8 + -16i + (2 * -4i + 4i * -4i)) = 0 (-8 + -16i + (-8i + -16i2)) = 0 Combine like terms: -16i + -8i = -24i (-8 + -24i + -16i2) = 0 Solving -8 + -24i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-8'. -8(1 + 3i + 2i2) = 0 Factor a trinomial. -8((1 + i)(1 + 2i)) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Subproblem 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, -0.5}
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