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Simplifying (3 + 2i) + z = (5 + -4i) Remove parenthesis around (3 + 2i) 3 + 2i + z = (5 + -4i) Remove parenthesis around (5 + -4i) 3 + 2i + z = 5 + -4i Solving 3 + 2i + z = 5 + -4i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4i' to each side of the equation. 3 + 2i + 4i + z = 5 + -4i + 4i Combine like terms: 2i + 4i = 6i 3 + 6i + z = 5 + -4i + 4i Combine like terms: -4i + 4i = 0 3 + 6i + z = 5 + 0 3 + 6i + z = 5 Add '-3' to each side of the equation. 3 + 6i + -3 + z = 5 + -3 Reorder the terms: 3 + -3 + 6i + z = 5 + -3 Combine like terms: 3 + -3 = 0 0 + 6i + z = 5 + -3 6i + z = 5 + -3 Combine like terms: 5 + -3 = 2 6i + z = 2 Add '-1z' to each side of the equation. 6i + z + -1z = 2 + -1z Combine like terms: z + -1z = 0 6i + 0 = 2 + -1z 6i = 2 + -1z Divide each side by '6'. i = 0.3333333333 + -0.1666666667z Simplifying i = 0.3333333333 + -0.1666666667z
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