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Simplifying (4 + -3i)(8 + i) = 0 Multiply (4 + -3i) * (8 + i) (4(8 + i) + -3i * (8 + i)) = 0 ((8 * 4 + i * 4) + -3i * (8 + i)) = 0 ((32 + 4i) + -3i * (8 + i)) = 0 (32 + 4i + (8 * -3i + i * -3i)) = 0 (32 + 4i + (-24i + -3i2)) = 0 Combine like terms: 4i + -24i = -20i (32 + -20i + -3i2) = 0 Solving 32 + -20i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -3i)(8 + i) = 0Subproblem 1
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 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 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Subproblem 2
Set the factor '(8 + i)' equal to zero and attempt to solve: Simplifying 8 + i = 0 Solving 8 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + i = 0 + -8 i = 0 + -8 Combine like terms: 0 + -8 = -8 i = -8 Simplifying i = -8Solution
i = {1.333333333, -8}
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