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Simplifying (6 + 4i) * z = 2i(z + 10) Reorder the terms for easier multiplication: z(6 + 4i) = 2i(z + 10) (6 * z + 4i * z) = 2i(z + 10) Reorder the terms: (4iz + 6z) = 2i(z + 10) (4iz + 6z) = 2i(z + 10) Reorder the terms: 4iz + 6z = 2i(10 + z) 4iz + 6z = (10 * 2i + z * 2i) 4iz + 6z = (20i + 2iz) Solving 4iz + 6z = 20i + 2iz Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-20i' to each side of the equation. 4iz + -20i + 6z = 20i + -20i + 2iz Reorder the terms: -20i + 4iz + 6z = 20i + -20i + 2iz Combine like terms: 20i + -20i = 0 -20i + 4iz + 6z = 0 + 2iz -20i + 4iz + 6z = 2iz Add '-2iz' to each side of the equation. -20i + 4iz + -2iz + 6z = 2iz + -2iz Combine like terms: 4iz + -2iz = 2iz -20i + 2iz + 6z = 2iz + -2iz Combine like terms: 2iz + -2iz = 0 -20i + 2iz + 6z = 0 Add '-6z' to each side of the equation. -20i + 2iz + 6z + -6z = 0 + -6z Combine like terms: 6z + -6z = 0 -20i + 2iz + 0 = 0 + -6z -20i + 2iz = 0 + -6z Remove the zero: -20i + 2iz = -6z Combine like terms: -6z + 6z = 0 -20i + 2iz + 6z = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10i + iz + 3z) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10i + iz + 3z)' equal to zero and attempt to solve: Simplifying -10i + iz + 3z = 0 Solving -10i + iz + 3z = 0 Move all terms containing i to the left, all other terms to the right. Add '-3z' to each side of the equation. -10i + iz + 3z + -3z = 0 + -3z Combine like terms: 3z + -3z = 0 -10i + iz + 0 = 0 + -3z -10i + iz = 0 + -3z Remove the zero: -10i + iz = -3z 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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