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Simplifying ((1 + 2i) * z2) + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 Reorder the terms for easier multiplication: (z2(1 + 2i)) + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 ((1 * z2 + 2i * z2)) + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 Reorder the terms: ((2iz2 + 1z2)) + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 ((2iz2 + 1z2)) + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 (2iz2 + 1z2) + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 Remove parenthesis around (2iz2 + 1z2) 2iz2 + 1z2 + (3(-1 + 3i) * z) + -1(8 + -1i) = 0 Reorder the terms for easier multiplication: 2iz2 + 1z2 + (3z(-1 + 3i)) + -1(8 + -1i) = 0 2iz2 + 1z2 + ((-1 * 3z + 3i * 3z)) + -1(8 + -1i) = 0 Reorder the terms: 2iz2 + 1z2 + ((9iz + -3z)) + -1(8 + -1i) = 0 2iz2 + 1z2 + ((9iz + -3z)) + -1(8 + -1i) = 0 2iz2 + 1z2 + (9iz + -3z) + -1(8 + -1i) = 0 Remove parenthesis around (9iz + -3z) 2iz2 + 1z2 + 9iz + -3z + -1(8 + -1i) = 0 2iz2 + 1z2 + 9iz + -3z + (8 * -1 + -1i * -1) = 0 2iz2 + 1z2 + 9iz + -3z + (-8 + 1i) = 0 Reorder the terms: -8 + 1i + 9iz + 2iz2 + -3z + 1z2 = 0 Solving -8 + 1i + 9iz + 2iz2 + -3z + 1z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 1i + 9iz + 2iz2 + -3z + 8 + 1z2 = 0 + 8 Reorder the terms: -8 + 8 + 1i + 9iz + 2iz2 + -3z + 1z2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 1i + 9iz + 2iz2 + -3z + 1z2 = 0 + 8 1i + 9iz + 2iz2 + -3z + 1z2 = 0 + 8 Combine like terms: 0 + 8 = 8 1i + 9iz + 2iz2 + -3z + 1z2 = 8 Add '3z' to each side of the equation. 1i + 9iz + 2iz2 + -3z + 3z + 1z2 = 8 + 3z Combine like terms: -3z + 3z = 0 1i + 9iz + 2iz2 + 0 + 1z2 = 8 + 3z 1i + 9iz + 2iz2 + 1z2 = 8 + 3z Add '-1z2' to each side of the equation. 1i + 9iz + 2iz2 + 1z2 + -1z2 = 8 + 3z + -1z2 Combine like terms: 1z2 + -1z2 = 0 1i + 9iz + 2iz2 + 0 = 8 + 3z + -1z2 1i + 9iz + 2iz2 = 8 + 3z + -1z2 Reorder the terms: -8 + 1i + 9iz + 2iz2 + -3z + z2 = 8 + 3z + -1z2 + -8 + -3z + z2 Reorder the terms: -8 + 1i + 9iz + 2iz2 + -3z + z2 = 8 + -8 + 3z + -3z + -1z2 + z2 Combine like terms: 8 + -8 = 0 -8 + 1i + 9iz + 2iz2 + -3z + z2 = 0 + 3z + -3z + -1z2 + z2 -8 + 1i + 9iz + 2iz2 + -3z + z2 = 3z + -3z + -1z2 + z2 Combine like terms: 3z + -3z = 0 -8 + 1i + 9iz + 2iz2 + -3z + z2 = 0 + -1z2 + z2 -8 + 1i + 9iz + 2iz2 + -3z + z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 -8 + 1i + 9iz + 2iz2 + -3z + z2 = 0 The solution to this equation could not be determined.
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