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Simplifying 7i(3 + -4i)(3 + 4i) = 0 Multiply (3 + -4i) * (3 + 4i) 7i(3(3 + 4i) + -4i * (3 + 4i)) = 0 7i((3 * 3 + 4i * 3) + -4i * (3 + 4i)) = 0 7i((9 + 12i) + -4i * (3 + 4i)) = 0 7i(9 + 12i + (3 * -4i + 4i * -4i)) = 0 7i(9 + 12i + (-12i + -16i2)) = 0 Combine like terms: 12i + -12i = 0 7i(9 + 0 + -16i2) = 0 7i(9 + -16i2) = 0 (9 * 7i + -16i2 * 7i) = 0 (63i + -112i3) = 0 Solving 63i + -112i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '7i'. 7i(9 + -16i2) = 0 Factor a difference between two squares. 7i((3 + 4i)(3 + -4i)) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 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 = -0.75Subproblem 3
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, -0.75, 0.75}
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