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Simplifying (-9 + 5i)(3 + i) = 0 Multiply (-9 + 5i) * (3 + i) (-9(3 + i) + 5i * (3 + i)) = 0 ((3 * -9 + i * -9) + 5i * (3 + i)) = 0 ((-27 + -9i) + 5i * (3 + i)) = 0 (-27 + -9i + (3 * 5i + i * 5i)) = 0 (-27 + -9i + (15i + 5i2)) = 0 Combine like terms: -9i + 15i = 6i (-27 + 6i + 5i2) = 0 Solving -27 + 6i + 5i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -1i)(9 + -5i) = 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 '(9 + -5i)' equal to zero and attempt to solve: Simplifying 9 + -5i = 0 Solving 9 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5i = 0 + -9 -5i = 0 + -9 Combine like terms: 0 + -9 = -9 -5i = -9 Divide each side by '-5'. i = 1.8 Simplifying i = 1.8Solution
i = {-3, 1.8}
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