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Simplifying (3 + 4i)(4 + -3i) = 0 Multiply (3 + 4i) * (4 + -3i) (3(4 + -3i) + 4i * (4 + -3i)) = 0 ((4 * 3 + -3i * 3) + 4i * (4 + -3i)) = 0 ((12 + -9i) + 4i * (4 + -3i)) = 0 (12 + -9i + (4 * 4i + -3i * 4i)) = 0 (12 + -9i + (16i + -12i2)) = 0 Combine like terms: -9i + 16i = 7i (12 + 7i + -12i2) = 0 Solving 12 + 7i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -3i)(3 + 4i) = 0Subproblem 1
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Subproblem 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 = {1.333333333, -0.75}
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