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Simplifying 13 + -13i + 7 = 5i + 15 + -10i + -3 Reorder the terms: 13 + 7 + -13i = 5i + 15 + -10i + -3 Combine like terms: 13 + 7 = 20 20 + -13i = 5i + 15 + -10i + -3 Reorder the terms: 20 + -13i = 15 + -3 + 5i + -10i Combine like terms: 15 + -3 = 12 20 + -13i = 12 + 5i + -10i Combine like terms: 5i + -10i = -5i 20 + -13i = 12 + -5i Solving 20 + -13i = 12 + -5i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5i' to each side of the equation. 20 + -13i + 5i = 12 + -5i + 5i Combine like terms: -13i + 5i = -8i 20 + -8i = 12 + -5i + 5i Combine like terms: -5i + 5i = 0 20 + -8i = 12 + 0 20 + -8i = 12 Add '-20' to each side of the equation. 20 + -20 + -8i = 12 + -20 Combine like terms: 20 + -20 = 0 0 + -8i = 12 + -20 -8i = 12 + -20 Combine like terms: 12 + -20 = -8 -8i = -8 Divide each side by '-8'. i = 1 Simplifying i = 1
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