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Simplifying a(4 + 5i)(4 + -5i)(4 + -3) = 0 Combine like terms: 4 + -3 = 1 a(4 + 5i)(4 + -5i)(1) = 0 Reorder the terms for easier multiplication: 1a(4 + 5i)(4 + -5i) = 0 Multiply (4 + 5i) * (4 + -5i) 1a(4(4 + -5i) + 5i * (4 + -5i)) = 0 1a((4 * 4 + -5i * 4) + 5i * (4 + -5i)) = 0 1a((16 + -20i) + 5i * (4 + -5i)) = 0 1a(16 + -20i + (4 * 5i + -5i * 5i)) = 0 1a(16 + -20i + (20i + -25i2)) = 0 Combine like terms: -20i + 20i = 0 1a(16 + 0 + -25i2) = 0 1a(16 + -25i2) = 0 (16 * 1a + -25i2 * 1a) = 0 (16a + -25ai2) = 0 Solving 16a + -25ai2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'a'. a(16 + -25i2) = 0 Factor a difference between two squares. a((4 + 5i)(4 + -5i)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Add '-5i' to each side of the equation. 5i + -5i = -4 + -5i Combine like terms: 5i + -5i = 0 0 = -4 + -5i Simplifying 0 = -4 + -5i The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + -5i)' equal to zero and attempt to solve: Simplifying 4 + -5i = 0 Solving 4 + -5i = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5i = 0 + -4 -5i = 0 + -4 Combine like terms: 0 + -4 = -4 -5i = -4 Add '5i' to each side of the equation. -5i + 5i = -4 + 5i Combine like terms: -5i + 5i = 0 0 = -4 + 5i Simplifying 0 = -4 + 5i The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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