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Simplifying (-9 + 8i)(6 + 8i) = 0 Multiply (-9 + 8i) * (6 + 8i) (-9(6 + 8i) + 8i * (6 + 8i)) = 0 ((6 * -9 + 8i * -9) + 8i * (6 + 8i)) = 0 ((-54 + -72i) + 8i * (6 + 8i)) = 0 (-54 + -72i + (6 * 8i + 8i * 8i)) = 0 (-54 + -72i + (48i + 64i2)) = 0 Combine like terms: -72i + 48i = -24i (-54 + -24i + 64i2) = 0 Solving -54 + -24i + 64i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -12i + 32i2) = 0 Factor a trinomial. 2((-3 + -4i)(9 + -8i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4i)' equal to zero and attempt to solve: Simplifying -3 + -4i = 0 Solving -3 + -4i = 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 + -4i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4i = 0 + 3 -4i = 0 + 3 Combine like terms: 0 + 3 = 3 -4i = 3 Divide each side by '-4'. i = -0.75 Simplifying i = -0.75Subproblem 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 = {-0.75, 1.125}
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