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Simplifying (-5 + 8i)(7 + -1i) = 0 Multiply (-5 + 8i) * (7 + -1i) (-5(7 + -1i) + 8i * (7 + -1i)) = 0 ((7 * -5 + -1i * -5) + 8i * (7 + -1i)) = 0 ((-35 + 5i) + 8i * (7 + -1i)) = 0 (-35 + 5i + (7 * 8i + -1i * 8i)) = 0 (-35 + 5i + (56i + -8i2)) = 0 Combine like terms: 5i + 56i = 61i (-35 + 61i + -8i2) = 0 Solving -35 + 61i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + i)(5 + -8i) = 0Subproblem 1
Set the factor '(-7 + i)' equal to zero and attempt to solve: Simplifying -7 + i = 0 Solving -7 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + i = 0 + 7 i = 0 + 7 Combine like terms: 0 + 7 = 7 i = 7 Simplifying i = 7Subproblem 2
Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625Solution
i = {7, 0.625}
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