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Simplifying (1 + 6i)(1 + 6i) = 0 Multiply (1 + 6i) * (1 + 6i) (1(1 + 6i) + 6i * (1 + 6i)) = 0 ((1 * 1 + 6i * 1) + 6i * (1 + 6i)) = 0 ((1 + 6i) + 6i * (1 + 6i)) = 0 (1 + 6i + (1 * 6i + 6i * 6i)) = 0 (1 + 6i + (6i + 36i2)) = 0 Combine like terms: 6i + 6i = 12i (1 + 12i + 36i2) = 0 Solving 1 + 12i + 36i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + 6i)(1 + 6i) = 0Subproblem 1
Set the factor '(1 + 6i)' equal to zero and attempt to solve: Simplifying 1 + 6i = 0 Solving 1 + 6i = 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 + 6i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6i = 0 + -1 6i = 0 + -1 Combine like terms: 0 + -1 = -1 6i = -1 Divide each side by '6'. i = -0.1666666667 Simplifying i = -0.1666666667Subproblem 2
Set the factor '(1 + 6i)' equal to zero and attempt to solve: Simplifying 1 + 6i = 0 Solving 1 + 6i = 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 + 6i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6i = 0 + -1 6i = 0 + -1 Combine like terms: 0 + -1 = -1 6i = -1 Divide each side by '6'. i = -0.1666666667 Simplifying i = -0.1666666667Solution
i = {-0.1666666667, -0.1666666667}
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