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Simplifying (6 + -4i)(6 + -4i) = 0 Multiply (6 + -4i) * (6 + -4i) (6(6 + -4i) + -4i * (6 + -4i)) = 0 ((6 * 6 + -4i * 6) + -4i * (6 + -4i)) = 0 ((36 + -24i) + -4i * (6 + -4i)) = 0 (36 + -24i + (6 * -4i + -4i * -4i)) = 0 (36 + -24i + (-24i + 16i2)) = 0 Combine like terms: -24i + -24i = -48i (36 + -48i + 16i2) = 0 Solving 36 + -48i + 16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -12i + 4i2) = 0 Factor a trinomial. 4((3 + -2i)(3 + -2i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {1.5, 1.5}
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