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Simplifying (9 + -2i)(8 + 5i) = 0 Multiply (9 + -2i) * (8 + 5i) (9(8 + 5i) + -2i * (8 + 5i)) = 0 ((8 * 9 + 5i * 9) + -2i * (8 + 5i)) = 0 ((72 + 45i) + -2i * (8 + 5i)) = 0 (72 + 45i + (8 * -2i + 5i * -2i)) = 0 (72 + 45i + (-16i + -10i2)) = 0 Combine like terms: 45i + -16i = 29i (72 + 29i + -10i2) = 0 Solving 72 + 29i + -10i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -2i)(8 + 5i) = 0Subproblem 1
Set the factor '(9 + -2i)' equal to zero and attempt to solve: Simplifying 9 + -2i = 0 Solving 9 + -2i = 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 + -2i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2i = 0 + -9 -2i = 0 + -9 Combine like terms: 0 + -9 = -9 -2i = -9 Divide each side by '-2'. i = 4.5 Simplifying i = 4.5Subproblem 2
Set the factor '(8 + 5i)' equal to zero and attempt to solve: Simplifying 8 + 5i = 0 Solving 8 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5i = 0 + -8 5i = 0 + -8 Combine like terms: 0 + -8 = -8 5i = -8 Divide each side by '5'. i = -1.6 Simplifying i = -1.6Solution
i = {4.5, -1.6}
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