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Simplifying (9 + -7i)(8 + 8i) = 0 Multiply (9 + -7i) * (8 + 8i) (9(8 + 8i) + -7i * (8 + 8i)) = 0 ((8 * 9 + 8i * 9) + -7i * (8 + 8i)) = 0 ((72 + 72i) + -7i * (8 + 8i)) = 0 (72 + 72i + (8 * -7i + 8i * -7i)) = 0 (72 + 72i + (-56i + -56i2)) = 0 Combine like terms: 72i + -56i = 16i (72 + 16i + -56i2) = 0 Solving 72 + 16i + -56i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8'. 8(9 + 2i + -7i2) = 0 Factor a trinomial. 8((9 + -7i)(1 + i)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(9 + -7i)' equal to zero and attempt to solve: Simplifying 9 + -7i = 0 Solving 9 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7i = 0 + -9 -7i = 0 + -9 Combine like terms: 0 + -9 = -9 -7i = -9 Divide each side by '-7'. i = 1.285714286 Simplifying i = 1.285714286Subproblem 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 = {1.285714286, -1}
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