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Simplifying 4i + -10i + 2 = 5(3 + -2i) + 7 Reorder the terms: 2 + 4i + -10i = 5(3 + -2i) + 7 Combine like terms: 4i + -10i = -6i 2 + -6i = 5(3 + -2i) + 7 2 + -6i = (3 * 5 + -2i * 5) + 7 2 + -6i = (15 + -10i) + 7 Reorder the terms: 2 + -6i = 15 + 7 + -10i Combine like terms: 15 + 7 = 22 2 + -6i = 22 + -10i Solving 2 + -6i = 22 + -10i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '10i' to each side of the equation. 2 + -6i + 10i = 22 + -10i + 10i Combine like terms: -6i + 10i = 4i 2 + 4i = 22 + -10i + 10i Combine like terms: -10i + 10i = 0 2 + 4i = 22 + 0 2 + 4i = 22 Add '-2' to each side of the equation. 2 + -2 + 4i = 22 + -2 Combine like terms: 2 + -2 = 0 0 + 4i = 22 + -2 4i = 22 + -2 Combine like terms: 22 + -2 = 20 4i = 20 Divide each side by '4'. i = 5 Simplifying i = 5
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