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Simplifying (7 + 8i)(7 + 8i) = 0 Multiply (7 + 8i) * (7 + 8i) (7(7 + 8i) + 8i * (7 + 8i)) = 0 ((7 * 7 + 8i * 7) + 8i * (7 + 8i)) = 0 ((49 + 56i) + 8i * (7 + 8i)) = 0 (49 + 56i + (7 * 8i + 8i * 8i)) = 0 (49 + 56i + (56i + 64i2)) = 0 Combine like terms: 56i + 56i = 112i (49 + 112i + 64i2) = 0 Solving 49 + 112i + 64i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 8i)(7 + 8i) = 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 '(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 = -0.875Solution
i = {-0.875, -0.875}
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