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Simplifying (2 + 4i)(-4 + -1i) = 0 Multiply (2 + 4i) * (-4 + -1i) (2(-4 + -1i) + 4i * (-4 + -1i)) = 0 ((-4 * 2 + -1i * 2) + 4i * (-4 + -1i)) = 0 ((-8 + -2i) + 4i * (-4 + -1i)) = 0 (-8 + -2i + (-4 * 4i + -1i * 4i)) = 0 (-8 + -2i + (-16i + -4i2)) = 0 Combine like terms: -2i + -16i = -18i (-8 + -18i + -4i2) = 0 Solving -8 + -18i + -4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 9i + 2i2) = 0 Factor a trinomial. -2((4 + i)(1 + 2i)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 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 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Subproblem 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 = {-4, -0.5}
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