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Simplifying (4 + 3i)(1 + -6i) = 0 Multiply (4 + 3i) * (1 + -6i) (4(1 + -6i) + 3i * (1 + -6i)) = 0 ((1 * 4 + -6i * 4) + 3i * (1 + -6i)) = 0 ((4 + -24i) + 3i * (1 + -6i)) = 0 (4 + -24i + (1 * 3i + -6i * 3i)) = 0 (4 + -24i + (3i + -18i2)) = 0 Combine like terms: -24i + 3i = -21i (4 + -21i + -18i2) = 0 Solving 4 + -21i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -6i)(4 + 3i) = 0Subproblem 1
Set the factor '(1 + -6i)' equal to zero and attempt to solve: Simplifying 1 + -6i = 0 Solving 1 + -6i = 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 + -6i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6i = 0 + -1 -6i = 0 + -1 Combine like terms: 0 + -1 = -1 -6i = -1 Divide each side by '-6'. i = 0.1666666667 Simplifying i = 0.1666666667Subproblem 2
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 = -1.333333333Solution
i = {0.1666666667, -1.333333333}
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