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Simplifying (1 + 3i)(1 + -4i) = 0 Multiply (1 + 3i) * (1 + -4i) (1(1 + -4i) + 3i * (1 + -4i)) = 0 ((1 * 1 + -4i * 1) + 3i * (1 + -4i)) = 0 ((1 + -4i) + 3i * (1 + -4i)) = 0 (1 + -4i + (1 * 3i + -4i * 3i)) = 0 (1 + -4i + (3i + -12i2)) = 0 Combine like terms: -4i + 3i = -1i (1 + -1i + -12i2) = 0 Solving 1 + -1i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -4i)(1 + 3i) = 0Subproblem 1
Set the factor '(1 + -4i)' equal to zero and attempt to solve: Simplifying 1 + -4i = 0 Solving 1 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i = 0 + -1 -4i = 0 + -1 Combine like terms: 0 + -1 = -1 -4i = -1 Divide each side by '-4'. i = 0.25 Simplifying i = 0.25Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve: Simplifying 1 + 3i = 0 Solving 1 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3i = 0 + -1 3i = 0 + -1 Combine like terms: 0 + -1 = -1 3i = -1 Divide each side by '3'. i = -0.3333333333 Simplifying i = -0.3333333333Solution
i = {0.25, -0.3333333333}
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