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Simplifying 4 + 2i + -1(a + 4i) = 9 + -2i 4 + 2i + (a * -1 + 4i * -1) = 9 + -2i 4 + 2i + (-1a + -4i) = 9 + -2i Reorder the terms: 4 + -1a + 2i + -4i = 9 + -2i Combine like terms: 2i + -4i = -2i 4 + -1a + -2i = 9 + -2i Add '2i' to each side of the equation. 4 + -1a + -2i + 2i = 9 + -2i + 2i Combine like terms: -2i + 2i = 0 4 + -1a + 0 = 9 + -2i + 2i 4 + -1a = 9 + -2i + 2i Combine like terms: -2i + 2i = 0 4 + -1a = 9 + 0 4 + -1a = 9 Solving 4 + -1a = 9 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 9 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 9 + -4 -1a = 9 + -4 Combine like terms: 9 + -4 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5
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