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Simplifying (7i + 7)(-3i + 8) = 0 Reorder the terms: (7 + 7i)(-3i + 8) = 0 Reorder the terms: (7 + 7i)(8 + -3i) = 0 Multiply (7 + 7i) * (8 + -3i) (7(8 + -3i) + 7i * (8 + -3i)) = 0 ((8 * 7 + -3i * 7) + 7i * (8 + -3i)) = 0 ((56 + -21i) + 7i * (8 + -3i)) = 0 (56 + -21i + (8 * 7i + -3i * 7i)) = 0 (56 + -21i + (56i + -21i2)) = 0 Combine like terms: -21i + 56i = 35i (56 + 35i + -21i2) = 0 Solving 56 + 35i + -21i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '7'. 7(8 + 5i + -3i2) = 0 Factor a trinomial. 7((8 + -3i)(1 + i)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(8 + -3i)' equal to zero and attempt to solve: Simplifying 8 + -3i = 0 Solving 8 + -3i = 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 + -3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3i = 0 + -8 -3i = 0 + -8 Combine like terms: 0 + -8 = -8 -3i = -8 Divide each side by '-3'. i = 2.666666667 Simplifying i = 2.666666667Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {2.666666667, -1}
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