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Simplifying (9 + -8i)(3 + -10i) = 0 Multiply (9 + -8i) * (3 + -10i) (9(3 + -10i) + -8i * (3 + -10i)) = 0 ((3 * 9 + -10i * 9) + -8i * (3 + -10i)) = 0 ((27 + -90i) + -8i * (3 + -10i)) = 0 (27 + -90i + (3 * -8i + -10i * -8i)) = 0 (27 + -90i + (-24i + 80i2)) = 0 Combine like terms: -90i + -24i = -114i (27 + -114i + 80i2) = 0 Solving 27 + -114i + 80i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -10i)(9 + -8i) = 0Subproblem 1
Set the factor '(3 + -10i)' equal to zero and attempt to solve: Simplifying 3 + -10i = 0 Solving 3 + -10i = 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 + -10i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10i = 0 + -3 -10i = 0 + -3 Combine like terms: 0 + -3 = -3 -10i = -3 Divide each side by '-10'. i = 0.3 Simplifying i = 0.3Subproblem 2
Set the factor '(9 + -8i)' equal to zero and attempt to solve: Simplifying 9 + -8i = 0 Solving 9 + -8i = 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 + -8i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8i = 0 + -9 -8i = 0 + -9 Combine like terms: 0 + -9 = -9 -8i = -9 Divide each side by '-8'. i = 1.125 Simplifying i = 1.125Solution
i = {0.3, 1.125}
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