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Simplifying z(3 + -2i) + (5 + -5i) = (1 + -1i) + z (3 * z + -2i * z) + (5 + -5i) = (1 + -1i) + z Reorder the terms: (-2iz + 3z) + (5 + -5i) = (1 + -1i) + z (-2iz + 3z) + (5 + -5i) = (1 + -1i) + z Remove parenthesis around (5 + -5i) -2iz + 3z + 5 + -5i = (1 + -1i) + z Reorder the terms: 5 + -5i + -2iz + 3z = (1 + -1i) + z Remove parenthesis around (1 + -1i) 5 + -5i + -2iz + 3z = 1 + -1i + z Solving 5 + -5i + -2iz + 3z = 1 + -1i + z 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. 5 + -5i + -2iz + i + 3z = 1 + -1i + i + z Reorder the terms: 5 + -5i + i + -2iz + 3z = 1 + -1i + i + z Combine like terms: -5i + i = -4i 5 + -4i + -2iz + 3z = 1 + -1i + i + z Combine like terms: -1i + i = 0 5 + -4i + -2iz + 3z = 1 + 0 + z 5 + -4i + -2iz + 3z = 1 + z Add '-5' to each side of the equation. 5 + -4i + -2iz + -5 + 3z = 1 + -5 + z Reorder the terms: 5 + -5 + -4i + -2iz + 3z = 1 + -5 + z Combine like terms: 5 + -5 = 0 0 + -4i + -2iz + 3z = 1 + -5 + z -4i + -2iz + 3z = 1 + -5 + z Combine like terms: 1 + -5 = -4 -4i + -2iz + 3z = -4 + z Add '-3z' to each side of the equation. -4i + -2iz + 3z + -3z = -4 + z + -3z Combine like terms: 3z + -3z = 0 -4i + -2iz + 0 = -4 + z + -3z -4i + -2iz = -4 + z + -3z Combine like terms: z + -3z = -2z -4i + -2iz = -4 + -2z Reorder the terms: 4 + -4i + -2iz + 2z = -4 + -2z + 4 + 2z Reorder the terms: 4 + -4i + -2iz + 2z = -4 + 4 + -2z + 2z Combine like terms: -4 + 4 = 0 4 + -4i + -2iz + 2z = 0 + -2z + 2z 4 + -4i + -2iz + 2z = -2z + 2z Combine like terms: -2z + 2z = 0 4 + -4i + -2iz + 2z = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -2i + -1iz + z) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -2i + -1iz + z)' equal to zero and attempt to solve: Simplifying 2 + -2i + -1iz + z = 0 Solving 2 + -2i + -1iz + z = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2i + -1iz + -2 + z = 0 + -2 Reorder the terms: 2 + -2 + -2i + -1iz + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2i + -1iz + z = 0 + -2 -2i + -1iz + z = 0 + -2 Combine like terms: 0 + -2 = -2 -2i + -1iz + z = -2 Add '-1z' to each side of the equation. -2i + -1iz + z + -1z = -2 + -1z Combine like terms: z + -1z = 0 -2i + -1iz + 0 = -2 + -1z -2i + -1iz = -2 + -1z 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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