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Simplifying 4b + -5 + (a + -3) * i = 7 + -8i Reorder the terms: 4b + -5 + (-3 + a) * i = 7 + -8i Reorder the terms for easier multiplication: 4b + -5 + i(-3 + a) = 7 + -8i 4b + -5 + (-3 * i + a * i) = 7 + -8i Reorder the terms: 4b + -5 + (ai + -3i) = 7 + -8i 4b + -5 + (ai + -3i) = 7 + -8i Reorder the terms: -5 + ai + 4b + -3i = 7 + -8i Solving -5 + ai + 4b + -3i = 7 + -8i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + ai + 4b + 5 + -3i = 7 + 5 + -8i Reorder the terms: -5 + 5 + ai + 4b + -3i = 7 + 5 + -8i Combine like terms: -5 + 5 = 0 0 + ai + 4b + -3i = 7 + 5 + -8i ai + 4b + -3i = 7 + 5 + -8i Combine like terms: 7 + 5 = 12 ai + 4b + -3i = 12 + -8i Add '-4b' to each side of the equation. ai + 4b + -4b + -3i = 12 + -4b + -8i Combine like terms: 4b + -4b = 0 ai + 0 + -3i = 12 + -4b + -8i ai + -3i = 12 + -4b + -8i Add '3i' to each side of the equation. ai + -3i + 3i = 12 + -4b + -8i + 3i Combine like terms: -3i + 3i = 0 ai + 0 = 12 + -4b + -8i + 3i ai = 12 + -4b + -8i + 3i Combine like terms: -8i + 3i = -5i ai = 12 + -4b + -5i Divide each side by 'i'. a = 12i-1 + -4bi-1 + -5 Simplifying a = 12i-1 + -4bi-1 + -5 Reorder the terms: a = -5 + -4bi-1 + 12i-1
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