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Simplifying i(4 + -5i)(1 + 2i) = 0 Multiply (4 + -5i) * (1 + 2i) i(4(1 + 2i) + -5i * (1 + 2i)) = 0 i((1 * 4 + 2i * 4) + -5i * (1 + 2i)) = 0 i((4 + 8i) + -5i * (1 + 2i)) = 0 i(4 + 8i + (1 * -5i + 2i * -5i)) = 0 i(4 + 8i + (-5i + -10i2)) = 0 Combine like terms: 8i + -5i = 3i i(4 + 3i + -10i2) = 0 (4 * i + 3i * i + -10i2 * i) = 0 (4i + 3i2 + -10i3) = 0 Solving 4i + 3i2 + -10i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'i'. i(4 + 3i + -10i2) = 0 Factor a trinomial. i((4 + -5i)(1 + 2i)) = 0Subproblem 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 '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 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 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {0, 0.8, -0.5}
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