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Simplifying (-2 + -6i)(6 + 7i) = 0 Multiply (-2 + -6i) * (6 + 7i) (-2(6 + 7i) + -6i * (6 + 7i)) = 0 ((6 * -2 + 7i * -2) + -6i * (6 + 7i)) = 0 ((-12 + -14i) + -6i * (6 + 7i)) = 0 (-12 + -14i + (6 * -6i + 7i * -6i)) = 0 (-12 + -14i + (-36i + -42i2)) = 0 Combine like terms: -14i + -36i = -50i (-12 + -50i + -42i2) = 0 Solving -12 + -50i + -42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 25i + 21i2) = 0 Factor a trinomial. -2((6 + 7i)(1 + 3i)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(6 + 7i)' equal to zero and attempt to solve: Simplifying 6 + 7i = 0 Solving 6 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7i = 0 + -6 7i = 0 + -6 Combine like terms: 0 + -6 = -6 7i = -6 Divide each side by '7'. i = -0.8571428571 Simplifying i = -0.8571428571Subproblem 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 = {-0.8571428571, -0.3333333333}
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