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Simplifying 2i(4 + -5i)(4 + 5i) = 0 Multiply (4 + -5i) * (4 + 5i) 2i(4(4 + 5i) + -5i * (4 + 5i)) = 0 2i((4 * 4 + 5i * 4) + -5i * (4 + 5i)) = 0 2i((16 + 20i) + -5i * (4 + 5i)) = 0 2i(16 + 20i + (4 * -5i + 5i * -5i)) = 0 2i(16 + 20i + (-20i + -25i2)) = 0 Combine like terms: 20i + -20i = 0 2i(16 + 0 + -25i2) = 0 2i(16 + -25i2) = 0 (16 * 2i + -25i2 * 2i) = 0 (32i + -50i3) = 0 Solving 32i + -50i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2i'. 2i(16 + -25i2) = 0 Factor a difference between two squares. 2i((4 + 5i)(4 + -5i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 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 i 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 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Subproblem 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 i 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 Divide each side by '-5'. i = 0.8 Simplifying i = 0.8Solution
i = {0, -0.8, 0.8}
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