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Simplifying -1i(5 + -1i) + 2i(i + 6) = 0 (5 * -1i + -1i * -1i) + 2i(i + 6) = 0 (-5i + 1i2) + 2i(i + 6) = 0 Reorder the terms: -5i + 1i2 + 2i(6 + i) = 0 -5i + 1i2 + (6 * 2i + i * 2i) = 0 -5i + 1i2 + (12i + 2i2) = 0 Reorder the terms: -5i + 12i + 1i2 + 2i2 = 0 Combine like terms: -5i + 12i = 7i 7i + 1i2 + 2i2 = 0 Combine like terms: 1i2 + 2i2 = 3i2 7i + 3i2 = 0 Solving 7i + 3i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'i'. i(7 + 3i) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(7 + 3i)' equal to zero and attempt to solve: Simplifying 7 + 3i = 0 Solving 7 + 3i = 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 + 3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3i = 0 + -7 3i = 0 + -7 Combine like terms: 0 + -7 = -7 3i = -7 Divide each side by '3'. i = -2.333333333 Simplifying i = -2.333333333Solution
i = {0, -2.333333333}
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