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Simplifying (6)(3i + 4)(1) + (4y + 1)(2i) = (8iy + 2i) + (18i + 24) Reorder the terms: 6(4 + 3i)(1) + (4y + 1)(2i) = (8iy + 2i) + (18i + 24) Reorder the terms for easier multiplication: 6 * 1(4 + 3i) + (4y + 1)(2i) = (8iy + 2i) + (18i + 24) Multiply 6 * 1 6(4 + 3i) + (4y + 1)(2i) = (8iy + 2i) + (18i + 24) (4 * 6 + 3i * 6) + (4y + 1)(2i) = (8iy + 2i) + (18i + 24) (24 + 18i) + (4y + 1)(2i) = (8iy + 2i) + (18i + 24) Reorder the terms: 24 + 18i + (1 + 4y)(2i) = (8iy + 2i) + (18i + 24) Remove parenthesis around (2i) 24 + 18i + (1 + 4y) * 2i = (8iy + 2i) + (18i + 24) Reorder the terms for easier multiplication: 24 + 18i + 2i(1 + 4y) = (8iy + 2i) + (18i + 24) 24 + 18i + (1 * 2i + 4y * 2i) = (8iy + 2i) + (18i + 24) 24 + 18i + (2i + 8iy) = (8iy + 2i) + (18i + 24) Combine like terms: 18i + 2i = 20i 24 + 20i + 8iy = (8iy + 2i) + (18i + 24) Reorder the terms: 24 + 20i + 8iy = (2i + 8iy) + (18i + 24) Remove parenthesis around (2i + 8iy) 24 + 20i + 8iy = 2i + 8iy + (18i + 24) Reorder the terms: 24 + 20i + 8iy = 2i + 8iy + (24 + 18i) Remove parenthesis around (24 + 18i) 24 + 20i + 8iy = 2i + 8iy + 24 + 18i Reorder the terms: 24 + 20i + 8iy = 24 + 2i + 18i + 8iy Combine like terms: 2i + 18i = 20i 24 + 20i + 8iy = 24 + 20i + 8iy Add '-24' to each side of the equation. 24 + 20i + -24 + 8iy = 24 + 20i + -24 + 8iy Reorder the terms: 24 + -24 + 20i + 8iy = 24 + 20i + -24 + 8iy Combine like terms: 24 + -24 = 0 0 + 20i + 8iy = 24 + 20i + -24 + 8iy 20i + 8iy = 24 + 20i + -24 + 8iy Reorder the terms: 20i + 8iy = 24 + -24 + 20i + 8iy Combine like terms: 24 + -24 = 0 20i + 8iy = 0 + 20i + 8iy 20i + 8iy = 20i + 8iy Add '-20i' to each side of the equation. 20i + -20i + 8iy = 20i + -20i + 8iy Combine like terms: 20i + -20i = 0 0 + 8iy = 20i + -20i + 8iy 8iy = 20i + -20i + 8iy Combine like terms: 20i + -20i = 0 8iy = 0 + 8iy 8iy = 8iy Add '-8iy' to each side of the equation. 8iy + -8iy = 8iy + -8iy Combine like terms: 8iy + -8iy = 0 0 = 8iy + -8iy Combine like terms: 8iy + -8iy = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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