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Simplifying (2 + i)(4 + -3i) = 0 Multiply (2 + i) * (4 + -3i) (2(4 + -3i) + i(4 + -3i)) = 0 ((4 * 2 + -3i * 2) + i(4 + -3i)) = 0 ((8 + -6i) + i(4 + -3i)) = 0 (8 + -6i + (4 * i + -3i * i)) = 0 (8 + -6i + (4i + -3i2)) = 0 Combine like terms: -6i + 4i = -2i (8 + -2i + -3i2) = 0 Solving 8 + -2i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -3i)(2 + 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 '(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 = {1.333333333, -2}
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