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Simplifying (4 + 4i)(3 + -7i) = 0 Multiply (4 + 4i) * (3 + -7i) (4(3 + -7i) + 4i * (3 + -7i)) = 0 ((3 * 4 + -7i * 4) + 4i * (3 + -7i)) = 0 ((12 + -28i) + 4i * (3 + -7i)) = 0 (12 + -28i + (3 * 4i + -7i * 4i)) = 0 (12 + -28i + (12i + -28i2)) = 0 Combine like terms: -28i + 12i = -16i (12 + -16i + -28i2) = 0 Solving 12 + -16i + -28i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -4i + -7i2) = 0 Factor a trinomial. 4((3 + -7i)(1 + i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve: Simplifying 3 + -7i = 0 Solving 3 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7i = 0 + -3 -7i = 0 + -3 Combine like terms: 0 + -3 = -3 -7i = -3 Divide each side by '-7'. i = 0.4285714286 Simplifying i = 0.4285714286Subproblem 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 = {0.4285714286, -1}
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