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Simplifying (4 + -5i)(-1 + -7i) = 0 Multiply (4 + -5i) * (-1 + -7i) (4(-1 + -7i) + -5i * (-1 + -7i)) = 0 ((-1 * 4 + -7i * 4) + -5i * (-1 + -7i)) = 0 ((-4 + -28i) + -5i * (-1 + -7i)) = 0 (-4 + -28i + (-1 * -5i + -7i * -5i)) = 0 (-4 + -28i + (5i + 35i2)) = 0 Combine like terms: -28i + 5i = -23i (-4 + -23i + 35i2) = 0 Solving -4 + -23i + 35i2 = 0 Solving for variable 'i'. Factor a trinomial. (-1 + -7i)(4 + -5i) = 0Subproblem 1
Set the factor '(-1 + -7i)' equal to zero and attempt to solve: Simplifying -1 + -7i = 0 Solving -1 + -7i = 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 + -7i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7i = 0 + 1 -7i = 0 + 1 Combine like terms: 0 + 1 = 1 -7i = 1 Divide each side by '-7'. i = -0.1428571429 Simplifying i = -0.1428571429Subproblem 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 = {-0.1428571429, 0.8}
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