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