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Simplifying a + ib = 3 + 3a + 3ib + 4i + 4ia + -4b Reorder the terms: a + bi = 3 + 3a + 4ai + -4b + 3bi + 4i Solving a + bi = 3 + 3a + 4ai + -4b + 3bi + 4i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. a + -3a + bi = 3 + 3a + 4ai + -4b + 3bi + -3a + 4i Combine like terms: a + -3a = -2a -2a + bi = 3 + 3a + 4ai + -4b + 3bi + -3a + 4i Reorder the terms: -2a + bi = 3 + 3a + -3a + 4ai + -4b + 3bi + 4i Combine like terms: 3a + -3a = 0 -2a + bi = 3 + 0 + 4ai + -4b + 3bi + 4i -2a + bi = 3 + 4ai + -4b + 3bi + 4i Add '-4ai' to each side of the equation. -2a + -4ai + bi = 3 + 4ai + -4b + 3bi + -4ai + 4i Reorder the terms: -2a + -4ai + bi = 3 + 4ai + -4ai + -4b + 3bi + 4i Combine like terms: 4ai + -4ai = 0 -2a + -4ai + bi = 3 + 0 + -4b + 3bi + 4i -2a + -4ai + bi = 3 + -4b + 3bi + 4i Add '-1bi' to each side of the equation. -2a + -4ai + bi + -1bi = 3 + -4b + 3bi + -1bi + 4i Combine like terms: bi + -1bi = 0 -2a + -4ai + 0 = 3 + -4b + 3bi + -1bi + 4i -2a + -4ai = 3 + -4b + 3bi + -1bi + 4i Combine like terms: 3bi + -1bi = 2bi -2a + -4ai = 3 + -4b + 2bi + 4i Reorder the terms: -3 + -2a + -4ai + 4b + -2bi + -4i = 3 + -4b + 2bi + 4i + -3 + 4b + -2bi + -4i Reorder the terms: -3 + -2a + -4ai + 4b + -2bi + -4i = 3 + -3 + -4b + 4b + 2bi + -2bi + 4i + -4i Combine like terms: 3 + -3 = 0 -3 + -2a + -4ai + 4b + -2bi + -4i = 0 + -4b + 4b + 2bi + -2bi + 4i + -4i -3 + -2a + -4ai + 4b + -2bi + -4i = -4b + 4b + 2bi + -2bi + 4i + -4i Combine like terms: -4b + 4b = 0 -3 + -2a + -4ai + 4b + -2bi + -4i = 0 + 2bi + -2bi + 4i + -4i -3 + -2a + -4ai + 4b + -2bi + -4i = 2bi + -2bi + 4i + -4i Combine like terms: 2bi + -2bi = 0 -3 + -2a + -4ai + 4b + -2bi + -4i = 0 + 4i + -4i -3 + -2a + -4ai + 4b + -2bi + -4i = 4i + -4i Combine like terms: 4i + -4i = 0 -3 + -2a + -4ai + 4b + -2bi + -4i = 0 The solution to this equation could not be determined.
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