z=(2-i)z

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Solution for z=(2-i)z equation:


Simplifying
z = (2 + -1i) * z

Reorder the terms for easier multiplication:
z = z(2 + -1i)
z = (2 * z + -1i * z)

Reorder the terms:
z = (-1iz + 2z)
z = (-1iz + 2z)

Solving
z = -1iz + 2z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add 'iz' to each side of the equation.
iz + z = -1iz + iz + 2z

Combine like terms: -1iz + iz = 0
iz + z = 0 + 2z
iz + z = 2z

Add '-2z' to each side of the equation.
iz + z + -2z = 2z + -2z

Combine like terms: z + -2z = -1z
iz + -1z = 2z + -2z

Combine like terms: 2z + -2z = 0
iz + -1z = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(i + -1) = 0

Subproblem 1

Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0

Subproblem 2

Set the factor '(i + -1)' equal to zero and attempt to solve: Simplifying i + -1 = 0 Reorder the terms: -1 + i = 0 Solving -1 + i = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + i = 0 + 1 i = 0 + 1 Combine like terms: 0 + 1 = 1 i = 1 Add '-1i' to each side of the equation. i + -1i = 1 + -1i Combine like terms: i + -1i = 0 0 = 1 + -1i Simplifying 0 = 1 + -1i The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

z = {0}

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