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Simplifying z = (2 + i)(4 + 4i + z) Multiply (2 + i) * (4 + 4i + z) z = (2(4 + 4i + z) + i(4 + 4i + z)) z = ((4 * 2 + 4i * 2 + z * 2) + i(4 + 4i + z)) z = ((8 + 8i + 2z) + i(4 + 4i + z)) z = (8 + 8i + 2z + (4 * i + 4i * i + z * i)) Reorder the terms: z = (8 + 8i + 2z + (4i + iz + 4i2)) z = (8 + 8i + 2z + (4i + iz + 4i2)) Reorder the terms: z = (8 + 8i + 4i + iz + 4i2 + 2z) Combine like terms: 8i + 4i = 12i z = (8 + 12i + iz + 4i2 + 2z) Solving z = 8 + 12i + iz + 4i2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1iz' to each side of the equation. -1iz + z = 8 + 12i + iz + 4i2 + -1iz + 2z Reorder the terms: -1iz + z = 8 + 12i + iz + -1iz + 4i2 + 2z Combine like terms: iz + -1iz = 0 -1iz + z = 8 + 12i + 0 + 4i2 + 2z -1iz + z = 8 + 12i + 4i2 + 2z Add '-2z' to each side of the equation. -1iz + z + -2z = 8 + 12i + 4i2 + 2z + -2z Combine like terms: z + -2z = -1z -1iz + -1z = 8 + 12i + 4i2 + 2z + -2z Combine like terms: 2z + -2z = 0 -1iz + -1z = 8 + 12i + 4i2 + 0 -1iz + -1z = 8 + 12i + 4i2 Reorder the terms: -8 + -12i + -1iz + -4i2 + -1z = 8 + 12i + 4i2 + -8 + -12i + -4i2 Reorder the terms: -8 + -12i + -1iz + -4i2 + -1z = 8 + -8 + 12i + -12i + 4i2 + -4i2 Combine like terms: 8 + -8 = 0 -8 + -12i + -1iz + -4i2 + -1z = 0 + 12i + -12i + 4i2 + -4i2 -8 + -12i + -1iz + -4i2 + -1z = 12i + -12i + 4i2 + -4i2 Combine like terms: 12i + -12i = 0 -8 + -12i + -1iz + -4i2 + -1z = 0 + 4i2 + -4i2 -8 + -12i + -1iz + -4i2 + -1z = 4i2 + -4i2 Combine like terms: 4i2 + -4i2 = 0 -8 + -12i + -1iz + -4i2 + -1z = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 12i + iz + 4i2 + z) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 12i + iz + 4i2 + z)' equal to zero and attempt to solve: Simplifying 8 + 12i + iz + 4i2 + z = 0 Solving 8 + 12i + iz + 4i2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 12i + iz + 4i2 + -8 + z = 0 + -8 Reorder the terms: 8 + -8 + 12i + iz + 4i2 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 12i + iz + 4i2 + z = 0 + -8 12i + iz + 4i2 + z = 0 + -8 Combine like terms: 0 + -8 = -8 12i + iz + 4i2 + z = -8 Add '-12i' to each side of the equation. 12i + iz + 4i2 + -12i + z = -8 + -12i Reorder the terms: 12i + -12i + iz + 4i2 + z = -8 + -12i Combine like terms: 12i + -12i = 0 0 + iz + 4i2 + z = -8 + -12i iz + 4i2 + z = -8 + -12i Add '-4i2' to each side of the equation. iz + 4i2 + -4i2 + z = -8 + -12i + -4i2 Combine like terms: 4i2 + -4i2 = 0 iz + 0 + z = -8 + -12i + -4i2 iz + z = -8 + -12i + -4i2 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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