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Simplifying (4 + -3i)(3 + -4i) = 0 Multiply (4 + -3i) * (3 + -4i) (4(3 + -4i) + -3i * (3 + -4i)) = 0 ((3 * 4 + -4i * 4) + -3i * (3 + -4i)) = 0 ((12 + -16i) + -3i * (3 + -4i)) = 0 (12 + -16i + (3 * -3i + -4i * -3i)) = 0 (12 + -16i + (-9i + 12i2)) = 0 Combine like terms: -16i + -9i = -25i (12 + -25i + 12i2) = 0 Solving 12 + -25i + 12i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -4i)(4 + -3i) = 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 '(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 = 1.333333333Solution
i = {0.75, 1.333333333}
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