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Simplifying (-1 + -4i)(1 + 4i) = 0 Multiply (-1 + -4i) * (1 + 4i) (-1(1 + 4i) + -4i * (1 + 4i)) = 0 ((1 * -1 + 4i * -1) + -4i * (1 + 4i)) = 0 ((-1 + -4i) + -4i * (1 + 4i)) = 0 (-1 + -4i + (1 * -4i + 4i * -4i)) = 0 (-1 + -4i + (-4i + -16i2)) = 0 Combine like terms: -4i + -4i = -8i (-1 + -8i + -16i2) = 0 Solving -1 + -8i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 8i + 16i2) = 0 Factor a trinomial. -1((1 + 4i)(1 + 4i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 4i)' equal to zero and attempt to solve: Simplifying 1 + 4i = 0 Solving 1 + 4i = 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 + 4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4i = 0 + -1 4i = 0 + -1 Combine like terms: 0 + -1 = -1 4i = -1 Divide each side by '4'. i = -0.25 Simplifying i = -0.25Subproblem 2
Set the factor '(1 + 4i)' equal to zero and attempt to solve: Simplifying 1 + 4i = 0 Solving 1 + 4i = 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 + 4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4i = 0 + -1 4i = 0 + -1 Combine like terms: 0 + -1 = -1 4i = -1 Divide each side by '4'. i = -0.25 Simplifying i = -0.25Solution
i = {-0.25, -0.25}
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