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Simplifying (8 + -5i)(3 + 3i) = 0 Multiply (8 + -5i) * (3 + 3i) (8(3 + 3i) + -5i * (3 + 3i)) = 0 ((3 * 8 + 3i * 8) + -5i * (3 + 3i)) = 0 ((24 + 24i) + -5i * (3 + 3i)) = 0 (24 + 24i + (3 * -5i + 3i * -5i)) = 0 (24 + 24i + (-15i + -15i2)) = 0 Combine like terms: 24i + -15i = 9i (24 + 9i + -15i2) = 0 Solving 24 + 9i + -15i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 3i + -5i2) = 0 Factor a trinomial. 3((8 + -5i)(1 + i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -5i)' equal to zero and attempt to solve: Simplifying 8 + -5i = 0 Solving 8 + -5i = 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 + -5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5i = 0 + -8 -5i = 0 + -8 Combine like terms: 0 + -8 = -8 -5i = -8 Divide each side by '-5'. i = 1.6 Simplifying i = 1.6Subproblem 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 = {1.6, -1}
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