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Simplifying (2 + 5i)(-1 + 4i) = 0 Multiply (2 + 5i) * (-1 + 4i) (2(-1 + 4i) + 5i * (-1 + 4i)) = 0 ((-1 * 2 + 4i * 2) + 5i * (-1 + 4i)) = 0 ((-2 + 8i) + 5i * (-1 + 4i)) = 0 (-2 + 8i + (-1 * 5i + 4i * 5i)) = 0 (-2 + 8i + (-5i + 20i2)) = 0 Combine like terms: 8i + -5i = 3i (-2 + 3i + 20i2) = 0 Solving -2 + 3i + 20i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + -5i)(1 + -4i) = 0Subproblem 1
Set the factor '(-2 + -5i)' equal to zero and attempt to solve: Simplifying -2 + -5i = 0 Solving -2 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5i = 0 + 2 -5i = 0 + 2 Combine like terms: 0 + 2 = 2 -5i = 2 Divide each side by '-5'. i = -0.4 Simplifying i = -0.4Subproblem 2
Set the factor '(1 + -4i)' equal to zero and attempt to solve: Simplifying 1 + -4i = 0 Solving 1 + -4i = 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 + -4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i = 0 + -1 -4i = 0 + -1 Combine like terms: 0 + -1 = -1 -4i = -1 Divide each side by '-4'. i = 0.25 Simplifying i = 0.25Solution
i = {-0.4, 0.25}
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