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Simplifying (-8 + 9i)(9 + i) = 0 Multiply (-8 + 9i) * (9 + i) (-8(9 + i) + 9i * (9 + i)) = 0 ((9 * -8 + i * -8) + 9i * (9 + i)) = 0 ((-72 + -8i) + 9i * (9 + i)) = 0 (-72 + -8i + (9 * 9i + i * 9i)) = 0 (-72 + -8i + (81i + 9i2)) = 0 Combine like terms: -8i + 81i = 73i (-72 + 73i + 9i2) = 0 Solving -72 + 73i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-9 + -1i)(8 + -9i) = 0Subproblem 1
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 = -9Subproblem 2
Set the factor '(8 + -9i)' equal to zero and attempt to solve: Simplifying 8 + -9i = 0 Solving 8 + -9i = 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 + -9i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9i = 0 + -8 -9i = 0 + -8 Combine like terms: 0 + -8 = -8 -9i = -8 Divide each side by '-9'. i = 0.8888888889 Simplifying i = 0.8888888889Solution
i = {-9, 0.8888888889}
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