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Simplifying (-3 + i)(5 + -4i) = 0 Multiply (-3 + i) * (5 + -4i) (-3(5 + -4i) + i(5 + -4i)) = 0 ((5 * -3 + -4i * -3) + i(5 + -4i)) = 0 ((-15 + 12i) + i(5 + -4i)) = 0 (-15 + 12i + (5 * i + -4i * i)) = 0 (-15 + 12i + (5i + -4i2)) = 0 Combine like terms: 12i + 5i = 17i (-15 + 17i + -4i2) = 0 Solving -15 + 17i + -4i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + i)(5 + -4i) = 0Subproblem 1
Set the factor '(-3 + i)' equal to zero and attempt to solve: Simplifying -3 + i = 0 Solving -3 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + i = 0 + 3 i = 0 + 3 Combine like terms: 0 + 3 = 3 i = 3 Simplifying i = 3Subproblem 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 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 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Solution
i = {3, 1.25}
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