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Simplifying (a + 1) + (a + b) * I = -2 + 5i Reorder the terms: (1 + a) + (a + b) * I = -2 + 5i Remove parenthesis around (1 + a) 1 + a + (a + b) * I = -2 + 5i Reorder the terms for easier multiplication: 1 + a + I(a + b) = -2 + 5i 1 + a + (a * I + b * I) = -2 + 5i 1 + a + (aI + bI) = -2 + 5i Solving 1 + a + aI + bI = -2 + 5i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + a + aI + -1 + bI = -2 + -1 + 5i Reorder the terms: 1 + -1 + a + aI + bI = -2 + -1 + 5i Combine like terms: 1 + -1 = 0 0 + a + aI + bI = -2 + -1 + 5i a + aI + bI = -2 + -1 + 5i Combine like terms: -2 + -1 = -3 a + aI + bI = -3 + 5i Add '-1bI' to each side of the equation. a + aI + bI + -1bI = -3 + -1bI + 5i Combine like terms: bI + -1bI = 0 a + aI + 0 = -3 + -1bI + 5i a + aI = -3 + -1bI + 5i Reorder the terms: 3 + a + aI + bI + -5i = -3 + -1bI + 5i + 3 + bI + -5i Reorder the terms: 3 + a + aI + bI + -5i = -3 + 3 + -1bI + bI + 5i + -5i Combine like terms: -3 + 3 = 0 3 + a + aI + bI + -5i = 0 + -1bI + bI + 5i + -5i 3 + a + aI + bI + -5i = -1bI + bI + 5i + -5i Combine like terms: -1bI + bI = 0 3 + a + aI + bI + -5i = 0 + 5i + -5i 3 + a + aI + bI + -5i = 5i + -5i Combine like terms: 5i + -5i = 0 3 + a + aI + bI + -5i = 0 The solution to this equation could not be determined.
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