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Simplifying 7(6 + -2i) = 5(-3i + 1) (6 * 7 + -2i * 7) = 5(-3i + 1) (42 + -14i) = 5(-3i + 1) Reorder the terms: 42 + -14i = 5(1 + -3i) 42 + -14i = (1 * 5 + -3i * 5) 42 + -14i = (5 + -15i) Solving 42 + -14i = 5 + -15i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '15i' to each side of the equation. 42 + -14i + 15i = 5 + -15i + 15i Combine like terms: -14i + 15i = 1i 42 + 1i = 5 + -15i + 15i Combine like terms: -15i + 15i = 0 42 + 1i = 5 + 0 42 + 1i = 5 Add '-42' to each side of the equation. 42 + -42 + 1i = 5 + -42 Combine like terms: 42 + -42 = 0 0 + 1i = 5 + -42 1i = 5 + -42 Combine like terms: 5 + -42 = -37 1i = -37 Divide each side by '1'. i = -37 Simplifying i = -37
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