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Simplifying (-2 + 5i)(-4 + 5i) = 0 Multiply (-2 + 5i) * (-4 + 5i) (-2(-4 + 5i) + 5i * (-4 + 5i)) = 0 ((-4 * -2 + 5i * -2) + 5i * (-4 + 5i)) = 0 ((8 + -10i) + 5i * (-4 + 5i)) = 0 (8 + -10i + (-4 * 5i + 5i * 5i)) = 0 (8 + -10i + (-20i + 25i2)) = 0 Combine like terms: -10i + -20i = -30i (8 + -30i + 25i2) = 0 Solving 8 + -30i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -5i)(4 + -5i) = 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 '(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 = {0.4, 0.8}
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