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Simplifying (6 + -8i)(6 + -8i) = 0 Multiply (6 + -8i) * (6 + -8i) (6(6 + -8i) + -8i * (6 + -8i)) = 0 ((6 * 6 + -8i * 6) + -8i * (6 + -8i)) = 0 ((36 + -48i) + -8i * (6 + -8i)) = 0 (36 + -48i + (6 * -8i + -8i * -8i)) = 0 (36 + -48i + (-48i + 64i2)) = 0 Combine like terms: -48i + -48i = -96i (36 + -96i + 64i2) = 0 Solving 36 + -96i + 64i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -24i + 16i2) = 0 Factor a trinomial. 4((3 + -4i)(3 + -4i)) = 0 Ignore the factor 4.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 '(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 = 0.75Solution
i = {0.75, 0.75}
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