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Simplifying (7 + -8i)(8 + 7i) = 0 Multiply (7 + -8i) * (8 + 7i) (7(8 + 7i) + -8i * (8 + 7i)) = 0 ((8 * 7 + 7i * 7) + -8i * (8 + 7i)) = 0 ((56 + 49i) + -8i * (8 + 7i)) = 0 (56 + 49i + (8 * -8i + 7i * -8i)) = 0 (56 + 49i + (-64i + -56i2)) = 0 Combine like terms: 49i + -64i = -15i (56 + -15i + -56i2) = 0 Solving 56 + -15i + -56i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -8i)(8 + 7i) = 0Subproblem 1
Set the factor '(7 + -8i)' equal to zero and attempt to solve: Simplifying 7 + -8i = 0 Solving 7 + -8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8i = 0 + -7 -8i = 0 + -7 Combine like terms: 0 + -7 = -7 -8i = -7 Divide each side by '-8'. i = 0.875 Simplifying i = 0.875Subproblem 2
Set the factor '(8 + 7i)' equal to zero and attempt to solve: Simplifying 8 + 7i = 0 Solving 8 + 7i = 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 + 7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7i = 0 + -8 7i = 0 + -8 Combine like terms: 0 + -8 = -8 7i = -8 Divide each side by '7'. i = -1.142857143 Simplifying i = -1.142857143Solution
i = {0.875, -1.142857143}
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