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Simplifying (4 + -5i)(7 + -8i) = 0 Multiply (4 + -5i) * (7 + -8i) (4(7 + -8i) + -5i * (7 + -8i)) = 0 ((7 * 4 + -8i * 4) + -5i * (7 + -8i)) = 0 ((28 + -32i) + -5i * (7 + -8i)) = 0 (28 + -32i + (7 * -5i + -8i * -5i)) = 0 (28 + -32i + (-35i + 40i2)) = 0 Combine like terms: -32i + -35i = -67i (28 + -67i + 40i2) = 0 Solving 28 + -67i + 40i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -5i)(7 + -8i) = 0Subproblem 1
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 2
Set the factor '(7 + -8i)' equal to zero and attempt to solve: Simplifying 7 + -8i = 0 Solving 7 + -8i = 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 + -8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8i = 0 + -7 -8i = 0 + -7 Combine like terms: 0 + -7 = -7 -8i = -7 Divide each side by '-8'. i = 0.875 Simplifying i = 0.875Solution
i = {0.8, 0.875}
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