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Simplifying (-8 + 5i)(-7 + 3i) = 0 Multiply (-8 + 5i) * (-7 + 3i) (-8(-7 + 3i) + 5i * (-7 + 3i)) = 0 ((-7 * -8 + 3i * -8) + 5i * (-7 + 3i)) = 0 ((56 + -24i) + 5i * (-7 + 3i)) = 0 (56 + -24i + (-7 * 5i + 3i * 5i)) = 0 (56 + -24i + (-35i + 15i2)) = 0 Combine like terms: -24i + -35i = -59i (56 + -59i + 15i2) = 0 Solving 56 + -59i + 15i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -5i)(7 + -3i) = 0Subproblem 1
Set the factor '(8 + -5i)' equal to zero and attempt to solve: Simplifying 8 + -5i = 0 Solving 8 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5i = 0 + -8 -5i = 0 + -8 Combine like terms: 0 + -8 = -8 -5i = -8 Divide each side by '-5'. i = 1.6 Simplifying i = 1.6Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve: Simplifying 7 + -3i = 0 Solving 7 + -3i = 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 + -3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3i = 0 + -7 -3i = 0 + -7 Combine like terms: 0 + -7 = -7 -3i = -7 Divide each side by '-3'. i = 2.333333333 Simplifying i = 2.333333333Solution
i = {1.6, 2.333333333}
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