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Simplifying 5i((4 + -1i)(4 + -1i)) = 0 Multiply (4 + -1i) * (4 + -1i) 5i((4(4 + -1i) + -1i * (4 + -1i))) = 0 5i(((4 * 4 + -1i * 4) + -1i * (4 + -1i))) = 0 5i(((16 + -4i) + -1i * (4 + -1i))) = 0 5i((16 + -4i + (4 * -1i + -1i * -1i))) = 0 5i((16 + -4i + (-4i + 1i2))) = 0 Combine like terms: -4i + -4i = -8i 5i((16 + -8i + 1i2)) = 0 (16 * 5i + -8i * 5i + 1i2 * 5i) = 0 (80i + -40i2 + 5i3) = 0 Solving 80i + -40i2 + 5i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '5i'. 5i(16 + -8i + i2) = 0 Factor a trinomial. 5i((4 + -1i)(4 + -1i)) = 0 Ignore the factor 5.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 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 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 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Subproblem 3
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 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 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {0, 4, 4}
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