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Simplifying (-9 + 4i)(8 + i) = 0 Multiply (-9 + 4i) * (8 + i) (-9(8 + i) + 4i * (8 + i)) = 0 ((8 * -9 + i * -9) + 4i * (8 + i)) = 0 ((-72 + -9i) + 4i * (8 + i)) = 0 (-72 + -9i + (8 * 4i + i * 4i)) = 0 (-72 + -9i + (32i + 4i2)) = 0 Combine like terms: -9i + 32i = 23i (-72 + 23i + 4i2) = 0 Solving -72 + 23i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (-8 + -1i)(9 + -4i) = 0Subproblem 1
Set the factor '(-8 + -1i)' equal to zero and attempt to solve: Simplifying -8 + -1i = 0 Solving -8 + -1i = 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 + -1i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1i = 0 + 8 -1i = 0 + 8 Combine like terms: 0 + 8 = 8 -1i = 8 Divide each side by '-1'. i = -8 Simplifying i = -8Subproblem 2
Set the factor '(9 + -4i)' equal to zero and attempt to solve: Simplifying 9 + -4i = 0 Solving 9 + -4i = 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 + -4i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4i = 0 + -9 -4i = 0 + -9 Combine like terms: 0 + -9 = -9 -4i = -9 Divide each side by '-4'. i = 2.25 Simplifying i = 2.25Solution
i = {-8, 2.25}
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