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Simplifying (4 + 3i)(7 + -7i) = 0 Multiply (4 + 3i) * (7 + -7i) (4(7 + -7i) + 3i * (7 + -7i)) = 0 ((7 * 4 + -7i * 4) + 3i * (7 + -7i)) = 0 ((28 + -28i) + 3i * (7 + -7i)) = 0 (28 + -28i + (7 * 3i + -7i * 3i)) = 0 (28 + -28i + (21i + -21i2)) = 0 Combine like terms: -28i + 21i = -7i (28 + -7i + -21i2) = 0 Solving 28 + -7i + -21i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '7'. 7(4 + -1i + -3i2) = 0 Factor a trinomial. 7((1 + -1i)(4 + 3i)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 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 = {1, -1.333333333}
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