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Simplifying (a + 6) + (b + 3) * i = 5 + 8i Reorder the terms: (6 + a) + (b + 3) * i = 5 + 8i Remove parenthesis around (6 + a) 6 + a + (b + 3) * i = 5 + 8i Reorder the terms: 6 + a + (3 + b) * i = 5 + 8i Reorder the terms for easier multiplication: 6 + a + i(3 + b) = 5 + 8i 6 + a + (3 * i + b * i) = 5 + 8i Reorder the terms: 6 + a + (bi + 3i) = 5 + 8i 6 + a + (bi + 3i) = 5 + 8i Solving 6 + a + bi + 3i = 5 + 8i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + a + bi + -6 + 3i = 5 + -6 + 8i Reorder the terms: 6 + -6 + a + bi + 3i = 5 + -6 + 8i Combine like terms: 6 + -6 = 0 0 + a + bi + 3i = 5 + -6 + 8i a + bi + 3i = 5 + -6 + 8i Combine like terms: 5 + -6 = -1 a + bi + 3i = -1 + 8i Add '-1bi' to each side of the equation. a + bi + -1bi + 3i = -1 + -1bi + 8i Combine like terms: bi + -1bi = 0 a + 0 + 3i = -1 + -1bi + 8i a + 3i = -1 + -1bi + 8i Add '-3i' to each side of the equation. a + 3i + -3i = -1 + -1bi + 8i + -3i Combine like terms: 3i + -3i = 0 a + 0 = -1 + -1bi + 8i + -3i a = -1 + -1bi + 8i + -3i Combine like terms: 8i + -3i = 5i a = -1 + -1bi + 5i Simplifying a = -1 + -1bi + 5i
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