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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 + -5i(-3 + -1a) = 7 + -8i 4b + (-3 * -5i + -1a * -5i) = 7 + -8i Reorder the terms: 4b + (5ai + 15i) = 7 + -8i 4b + (5ai + 15i) = 7 + -8i Reorder the terms: 5ai + 4b + 15i = 7 + -8i Solving 5ai + 4b + 15i = 7 + -8i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 5ai + 4b + -4b + 15i = 7 + -4b + -8i Combine like terms: 4b + -4b = 0 5ai + 0 + 15i = 7 + -4b + -8i 5ai + 15i = 7 + -4b + -8i Add '-15i' to each side of the equation. 5ai + 15i + -15i = 7 + -4b + -8i + -15i Combine like terms: 15i + -15i = 0 5ai + 0 = 7 + -4b + -8i + -15i 5ai = 7 + -4b + -8i + -15i Combine like terms: -8i + -15i = -23i 5ai = 7 + -4b + -23i Divide each side by '5i'. a = 1.4i-1 + -0.8bi-1 + -4.6 Simplifying a = 1.4i-1 + -0.8bi-1 + -4.6 Reorder the terms: a = -4.6 + -0.8bi-1 + 1.4i-1
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