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Simplifying (2 + -3i)(1 + 4i) = 0 Multiply (2 + -3i) * (1 + 4i) (2(1 + 4i) + -3i * (1 + 4i)) = 0 ((1 * 2 + 4i * 2) + -3i * (1 + 4i)) = 0 ((2 + 8i) + -3i * (1 + 4i)) = 0 (2 + 8i + (1 * -3i + 4i * -3i)) = 0 (2 + 8i + (-3i + -12i2)) = 0 Combine like terms: 8i + -3i = 5i (2 + 5i + -12i2) = 0 Solving 2 + 5i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(1 + 4i) = 0Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
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 = -0.25Solution
i = {0.6666666667, -0.25}
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