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Simplifying 4b + -5 + (-1a + 3) * i = 7 + -8i Reorder the terms: 4b + -5 + (3 + -1a) * i = 7 + -8i Reorder the terms for easier multiplication: 4b + -5 + i(3 + -1a) = 7 + -8i 4b + -5 + (3 * i + -1a * i) = 7 + -8i Reorder the terms: 4b + -5 + (-1ai + 3i) = 7 + -8i 4b + -5 + (-1ai + 3i) = 7 + -8i Reorder the terms: -5 + -1ai + 4b + 3i = 7 + -8i Solving -5 + -1ai + 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 + -1ai + 4b + 5 + 3i = 7 + 5 + -8i Reorder the terms: -5 + 5 + -1ai + 4b + 3i = 7 + 5 + -8i Combine like terms: -5 + 5 = 0 0 + -1ai + 4b + 3i = 7 + 5 + -8i -1ai + 4b + 3i = 7 + 5 + -8i Combine like terms: 7 + 5 = 12 -1ai + 4b + 3i = 12 + -8i Add '-4b' to each side of the equation. -1ai + 4b + -4b + 3i = 12 + -4b + -8i Combine like terms: 4b + -4b = 0 -1ai + 0 + 3i = 12 + -4b + -8i -1ai + 3i = 12 + -4b + -8i Add '-3i' to each side of the equation. -1ai + 3i + -3i = 12 + -4b + -8i + -3i Combine like terms: 3i + -3i = 0 -1ai + 0 = 12 + -4b + -8i + -3i -1ai = 12 + -4b + -8i + -3i Combine like terms: -8i + -3i = -11i -1ai = 12 + -4b + -11i Divide each side by '-1i'. a = -12i-1 + 4bi-1 + 11 Simplifying a = -12i-1 + 4bi-1 + 11 Reorder the terms: a = 11 + 4bi-1 + -12i-1
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