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Simplifying (2x + -5) * i + -4y + 1 = 3 + -1i Reorder the terms: (-5 + 2x) * i + -4y + 1 = 3 + -1i Reorder the terms for easier multiplication: i(-5 + 2x) + -4y + 1 = 3 + -1i (-5 * i + 2x * i) + -4y + 1 = 3 + -1i (-5i + 2ix) + -4y + 1 = 3 + -1i Reorder the terms: 1 + -5i + 2ix + -4y = 3 + -1i Solving 1 + -5i + 2ix + -4y = 3 + -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. 1 + -5i + 2ix + i + -4y = 3 + -1i + i Reorder the terms: 1 + -5i + i + 2ix + -4y = 3 + -1i + i Combine like terms: -5i + i = -4i 1 + -4i + 2ix + -4y = 3 + -1i + i Combine like terms: -1i + i = 0 1 + -4i + 2ix + -4y = 3 + 0 1 + -4i + 2ix + -4y = 3 Add '-1' to each side of the equation. 1 + -4i + 2ix + -1 + -4y = 3 + -1 Reorder the terms: 1 + -1 + -4i + 2ix + -4y = 3 + -1 Combine like terms: 1 + -1 = 0 0 + -4i + 2ix + -4y = 3 + -1 -4i + 2ix + -4y = 3 + -1 Combine like terms: 3 + -1 = 2 -4i + 2ix + -4y = 2 Add '4y' to each side of the equation. -4i + 2ix + -4y + 4y = 2 + 4y Combine like terms: -4y + 4y = 0 -4i + 2ix + 0 = 2 + 4y -4i + 2ix = 2 + 4y Reorder the terms: -2 + -4i + 2ix + -4y = 2 + 4y + -2 + -4y Reorder the terms: -2 + -4i + 2ix + -4y = 2 + -2 + 4y + -4y Combine like terms: 2 + -2 = 0 -2 + -4i + 2ix + -4y = 0 + 4y + -4y -2 + -4i + 2ix + -4y = 4y + -4y Combine like terms: 4y + -4y = 0 -2 + -4i + 2ix + -4y = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2i + ix + -2y) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2i + ix + -2y)' equal to zero and attempt to solve: Simplifying -1 + -2i + ix + -2y = 0 Solving -1 + -2i + ix + -2y = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2i + ix + 1 + -2y = 0 + 1 Reorder the terms: -1 + 1 + -2i + ix + -2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2i + ix + -2y = 0 + 1 -2i + ix + -2y = 0 + 1 Combine like terms: 0 + 1 = 1 -2i + ix + -2y = 1 Add '2y' to each side of the equation. -2i + ix + -2y + 2y = 1 + 2y Combine like terms: -2y + 2y = 0 -2i + ix + 0 = 1 + 2y -2i + ix = 1 + 2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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