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Simplifying (-5 + 4i)(3 + i) = 0 Multiply (-5 + 4i) * (3 + i) (-5(3 + i) + 4i * (3 + i)) = 0 ((3 * -5 + i * -5) + 4i * (3 + i)) = 0 ((-15 + -5i) + 4i * (3 + i)) = 0 (-15 + -5i + (3 * 4i + i * 4i)) = 0 (-15 + -5i + (12i + 4i2)) = 0 Combine like terms: -5i + 12i = 7i (-15 + 7i + 4i2) = 0 Solving -15 + 7i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -1i)(5 + -4i) = 0Subproblem 1
Set the factor '(-3 + -1i)' equal to zero and attempt to solve: Simplifying -3 + -1i = 0 Solving -3 + -1i = 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 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. 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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