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Simplifying (2 + 4i)(-2 + -4i) = 0 Multiply (2 + 4i) * (-2 + -4i) (2(-2 + -4i) + 4i * (-2 + -4i)) = 0 ((-2 * 2 + -4i * 2) + 4i * (-2 + -4i)) = 0 ((-4 + -8i) + 4i * (-2 + -4i)) = 0 (-4 + -8i + (-2 * 4i + -4i * 4i)) = 0 (-4 + -8i + (-8i + -16i2)) = 0 Combine like terms: -8i + -8i = -16i (-4 + -16i + -16i2) = 0 Solving -4 + -16i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-4'. -4(1 + 4i + 4i2) = 0 Factor a trinomial. -4((1 + 2i)(1 + 2i)) = 0 Ignore the factor -4.Subproblem 1
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 = -0.5Subproblem 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 = {-0.5, -0.5}
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