a(4+5i)(4-5i)(4-3)=

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Solution for a(4+5i)(4-5i)(4-3)= equation:


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)) = 0

Subproblem 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 = 0

Subproblem 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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