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Simplifying (-2 + -1i)(4 + i) = 0 Multiply (-2 + -1i) * (4 + i) (-2(4 + i) + -1i * (4 + i)) = 0 ((4 * -2 + i * -2) + -1i * (4 + i)) = 0 ((-8 + -2i) + -1i * (4 + i)) = 0 (-8 + -2i + (4 * -1i + i * -1i)) = 0 (-8 + -2i + (-4i + -1i2)) = 0 Combine like terms: -2i + -4i = -6i (-8 + -6i + -1i2) = 0 Solving -8 + -6i + -1i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 6i + i2) = 0 Factor a trinomial. -1((4 + i)(2 + i)) = 0 Ignore the factor -1.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 '(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 = {-4, -2}
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