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Simplifying (a + -1) + (b + 3) * i = 8 + 7i Reorder the terms: (-1 + a) + (b + 3) * i = 8 + 7i Remove parenthesis around (-1 + a) -1 + a + (b + 3) * i = 8 + 7i Reorder the terms: -1 + a + (3 + b) * i = 8 + 7i Reorder the terms for easier multiplication: -1 + a + i(3 + b) = 8 + 7i -1 + a + (3 * i + b * i) = 8 + 7i Reorder the terms: -1 + a + (bi + 3i) = 8 + 7i -1 + a + (bi + 3i) = 8 + 7i Solving -1 + a + bi + 3i = 8 + 7i 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 + bi + 1 + 3i = 8 + 1 + 7i Reorder the terms: -1 + 1 + a + bi + 3i = 8 + 1 + 7i Combine like terms: -1 + 1 = 0 0 + a + bi + 3i = 8 + 1 + 7i a + bi + 3i = 8 + 1 + 7i Combine like terms: 8 + 1 = 9 a + bi + 3i = 9 + 7i Add '-1bi' to each side of the equation. a + bi + -1bi + 3i = 9 + -1bi + 7i Combine like terms: bi + -1bi = 0 a + 0 + 3i = 9 + -1bi + 7i a + 3i = 9 + -1bi + 7i Add '-3i' to each side of the equation. a + 3i + -3i = 9 + -1bi + 7i + -3i Combine like terms: 3i + -3i = 0 a + 0 = 9 + -1bi + 7i + -3i a = 9 + -1bi + 7i + -3i Combine like terms: 7i + -3i = 4i a = 9 + -1bi + 4i Simplifying a = 9 + -1bi + 4i
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