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Simplifying (-1 + 3i)(4 + i) = 0 Multiply (-1 + 3i) * (4 + i) (-1(4 + i) + 3i * (4 + i)) = 0 ((4 * -1 + i * -1) + 3i * (4 + i)) = 0 ((-4 + -1i) + 3i * (4 + i)) = 0 (-4 + -1i + (4 * 3i + i * 3i)) = 0 (-4 + -1i + (12i + 3i2)) = 0 Combine like terms: -1i + 12i = 11i (-4 + 11i + 3i2) = 0 Solving -4 + 11i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -1i)(1 + -3i) = 0Subproblem 1
Set the factor '(-4 + -1i)' equal to zero and attempt to solve: Simplifying -4 + -1i = 0 Solving -4 + -1i = 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 + -1i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1i = 0 + 4 -1i = 0 + 4 Combine like terms: 0 + 4 = 4 -1i = 4 Divide each side by '-1'. i = -4 Simplifying i = -4Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {-4, 0.3333333333}
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