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Simplifying (9 + -4i)(3 + -4i) = 0 Multiply (9 + -4i) * (3 + -4i) (9(3 + -4i) + -4i * (3 + -4i)) = 0 ((3 * 9 + -4i * 9) + -4i * (3 + -4i)) = 0 ((27 + -36i) + -4i * (3 + -4i)) = 0 (27 + -36i + (3 * -4i + -4i * -4i)) = 0 (27 + -36i + (-12i + 16i2)) = 0 Combine like terms: -36i + -12i = -48i (27 + -48i + 16i2) = 0 Solving 27 + -48i + 16i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -4i)(9 + -4i) = 0Subproblem 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 + -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 = {0.75, 2.25}
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