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Simplifying (-5 + i)(7 + -9i) = 0 Multiply (-5 + i) * (7 + -9i) (-5(7 + -9i) + i(7 + -9i)) = 0 ((7 * -5 + -9i * -5) + i(7 + -9i)) = 0 ((-35 + 45i) + i(7 + -9i)) = 0 (-35 + 45i + (7 * i + -9i * i)) = 0 (-35 + 45i + (7i + -9i2)) = 0 Combine like terms: 45i + 7i = 52i (-35 + 52i + -9i2) = 0 Solving -35 + 52i + -9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + i)(7 + -9i) = 0Subproblem 1
Set the factor '(-5 + i)' equal to zero and attempt to solve: Simplifying -5 + i = 0 Solving -5 + i = 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 + i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + i = 0 + 5 i = 0 + 5 Combine like terms: 0 + 5 = 5 i = 5 Simplifying i = 5Subproblem 2
Set the factor '(7 + -9i)' equal to zero and attempt to solve: Simplifying 7 + -9i = 0 Solving 7 + -9i = 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 + -9i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9i = 0 + -7 -9i = 0 + -7 Combine like terms: 0 + -7 = -7 -9i = -7 Divide each side by '-9'. i = 0.7777777778 Simplifying i = 0.7777777778Solution
i = {5, 0.7777777778}
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