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Simplifying (1 + 8i)(1 + 8i) = 0 Multiply (1 + 8i) * (1 + 8i) (1(1 + 8i) + 8i * (1 + 8i)) = 0 ((1 * 1 + 8i * 1) + 8i * (1 + 8i)) = 0 ((1 + 8i) + 8i * (1 + 8i)) = 0 (1 + 8i + (1 * 8i + 8i * 8i)) = 0 (1 + 8i + (8i + 64i2)) = 0 Combine like terms: 8i + 8i = 16i (1 + 16i + 64i2) = 0 Solving 1 + 16i + 64i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + 8i)(1 + 8i) = 0Subproblem 1
Set the factor '(1 + 8i)' equal to zero and attempt to solve: Simplifying 1 + 8i = 0 Solving 1 + 8i = 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 + 8i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8i = 0 + -1 8i = 0 + -1 Combine like terms: 0 + -1 = -1 8i = -1 Divide each side by '8'. i = -0.125 Simplifying i = -0.125Subproblem 2
Set the factor '(1 + 8i)' equal to zero and attempt to solve: Simplifying 1 + 8i = 0 Solving 1 + 8i = 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 + 8i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8i = 0 + -1 8i = 0 + -1 Combine like terms: 0 + -1 = -1 8i = -1 Divide each side by '8'. i = -0.125 Simplifying i = -0.125Solution
i = {-0.125, -0.125}
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