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Simplifying (-2 + 6i)(-2 + 6i) = 0 Multiply (-2 + 6i) * (-2 + 6i) (-2(-2 + 6i) + 6i * (-2 + 6i)) = 0 ((-2 * -2 + 6i * -2) + 6i * (-2 + 6i)) = 0 ((4 + -12i) + 6i * (-2 + 6i)) = 0 (4 + -12i + (-2 * 6i + 6i * 6i)) = 0 (4 + -12i + (-12i + 36i2)) = 0 Combine like terms: -12i + -12i = -24i (4 + -24i + 36i2) = 0 Solving 4 + -24i + 36i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -6i + 9i2) = 0 Factor a trinomial. 4((1 + -3i)(1 + -3i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {0.3333333333, 0.3333333333}
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