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Simplifying 0 = (1 + -3i) * x(-2 + 5i) Reorder the terms for easier multiplication: 0 = x(1 + -3i)(-2 + 5i) Multiply (1 + -3i) * (-2 + 5i) 0 = x(1(-2 + 5i) + -3i * (-2 + 5i)) 0 = x((-2 * 1 + 5i * 1) + -3i * (-2 + 5i)) 0 = x((-2 + 5i) + -3i * (-2 + 5i)) 0 = x(-2 + 5i + (-2 * -3i + 5i * -3i)) 0 = x(-2 + 5i + (6i + -15i2)) Combine like terms: 5i + 6i = 11i 0 = x(-2 + 11i + -15i2) 0 = (-2 * x + 11i * x + -15i2 * x) Reorder the terms: 0 = (11ix + -15i2x + -2x) 0 = (11ix + -15i2x + -2x) Solving 0 = 11ix + -15i2x + -2x Solving for variable 'i'. Remove the zero: -11ix + 15i2x + 2x = 11ix + -15i2x + -2x + -11ix + 15i2x + 2x Reorder the terms: -11ix + 15i2x + 2x = 11ix + -11ix + -15i2x + 15i2x + -2x + 2x Combine like terms: 11ix + -11ix = 0 -11ix + 15i2x + 2x = 0 + -15i2x + 15i2x + -2x + 2x -11ix + 15i2x + 2x = -15i2x + 15i2x + -2x + 2x Combine like terms: -15i2x + 15i2x = 0 -11ix + 15i2x + 2x = 0 + -2x + 2x -11ix + 15i2x + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 -11ix + 15i2x + 2x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11i + 15i2 + 2) = 0 Factor a trinomial. x((5i + -2)(3i + -1)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5i + -2)' equal to zero and attempt to solve: Simplifying 5i + -2 = 0 Reorder the terms: -2 + 5i = 0 Solving -2 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 5i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5i = 0 + 2 5i = 0 + 2 Combine like terms: 0 + 2 = 2 5i = 2 Divide each side by '5'. i = 0.4 Simplifying i = 0.4Subproblem 3
Set the factor '(3i + -1)' equal to zero and attempt to solve: Simplifying 3i + -1 = 0 Reorder the terms: -1 + 3i = 0 Solving -1 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 3i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3i = 0 + 1 3i = 0 + 1 Combine like terms: 0 + 1 = 1 3i = 1 Divide each side by '3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {0.4, 0.3333333333}
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