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Simplifying (9 + 8i)(-9 + i) = 0 Multiply (9 + 8i) * (-9 + i) (9(-9 + i) + 8i * (-9 + i)) = 0 ((-9 * 9 + i * 9) + 8i * (-9 + i)) = 0 ((-81 + 9i) + 8i * (-9 + i)) = 0 (-81 + 9i + (-9 * 8i + i * 8i)) = 0 (-81 + 9i + (-72i + 8i2)) = 0 Combine like terms: 9i + -72i = -63i (-81 + -63i + 8i2) = 0 Solving -81 + -63i + 8i2 = 0 Solving for variable 'i'. Factor a trinomial. (-9 + -8i)(9 + -1i) = 0Subproblem 1
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 = -1.125Subproblem 2
Set the factor '(9 + -1i)' equal to zero and attempt to solve: Simplifying 9 + -1i = 0 Solving 9 + -1i = 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 + -1i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i = 0 + -9 -1i = 0 + -9 Combine like terms: 0 + -9 = -9 -1i = -9 Divide each side by '-1'. i = 9 Simplifying i = 9Solution
i = {-1.125, 9}
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