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Simplifying 10i + 4 + -3i = 2i + 22 + -1(-7) Reorder the terms: 4 + 10i + -3i = 2i + 22 + -1(-7) Combine like terms: 10i + -3i = 7i 4 + 7i = 2i + 22 + -1(-7) Multiply -1 * -7 4 + 7i = 2i + 22 + 7 Reorder the terms: 4 + 7i = 22 + 7 + 2i Combine like terms: 22 + 7 = 29 4 + 7i = 29 + 2i Solving 4 + 7i = 29 + 2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2i' to each side of the equation. 4 + 7i + -2i = 29 + 2i + -2i Combine like terms: 7i + -2i = 5i 4 + 5i = 29 + 2i + -2i Combine like terms: 2i + -2i = 0 4 + 5i = 29 + 0 4 + 5i = 29 Add '-4' to each side of the equation. 4 + -4 + 5i = 29 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 29 + -4 5i = 29 + -4 Combine like terms: 29 + -4 = 25 5i = 25 Divide each side by '5'. i = 5 Simplifying i = 5
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