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Simplifying (-7 + 4i) + -1(3 + -2i) + -1(-12 + 2i) = 0 Remove parenthesis around (-7 + 4i) -7 + 4i + -1(3 + -2i) + -1(-12 + 2i) = 0 -7 + 4i + (3 * -1 + -2i * -1) + -1(-12 + 2i) = 0 -7 + 4i + (-3 + 2i) + -1(-12 + 2i) = 0 -7 + 4i + -3 + 2i + (-12 * -1 + 2i * -1) = 0 -7 + 4i + -3 + 2i + (12 + -2i) = 0 Reorder the terms: -7 + -3 + 12 + 4i + 2i + -2i = 0 Combine like terms: -7 + -3 = -10 -10 + 12 + 4i + 2i + -2i = 0 Combine like terms: -10 + 12 = 2 2 + 4i + 2i + -2i = 0 Combine like terms: 4i + 2i = 6i 2 + 6i + -2i = 0 Combine like terms: 6i + -2i = 4i 2 + 4i = 0 Solving 2 + 4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 4i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4i = 0 + -2 4i = 0 + -2 Combine like terms: 0 + -2 = -2 4i = -2 Divide each side by '4'. i = -0.5 Simplifying i = -0.5
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