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Simplifying (30 + -1i) + -1(18 + 6i) + 30i = 0 Remove parenthesis around (30 + -1i) 30 + -1i + -1(18 + 6i) + 30i = 0 30 + -1i + (18 * -1 + 6i * -1) + 30i = 0 30 + -1i + (-18 + -6i) + 30i = 0 Reorder the terms: 30 + -18 + -1i + -6i + 30i = 0 Combine like terms: 30 + -18 = 12 12 + -1i + -6i + 30i = 0 Combine like terms: -1i + -6i = -7i 12 + -7i + 30i = 0 Combine like terms: -7i + 30i = 23i 12 + 23i = 0 Solving 12 + 23i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 23i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 23i = 0 + -12 23i = 0 + -12 Combine like terms: 0 + -12 = -12 23i = -12 Divide each side by '23'. i = -0.5217391304 Simplifying i = -0.5217391304
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