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Simplifying (1 + -3i)(7 + 11i) = 0 Multiply (1 + -3i) * (7 + 11i) (1(7 + 11i) + -3i * (7 + 11i)) = 0 ((7 * 1 + 11i * 1) + -3i * (7 + 11i)) = 0 ((7 + 11i) + -3i * (7 + 11i)) = 0 (7 + 11i + (7 * -3i + 11i * -3i)) = 0 (7 + 11i + (-21i + -33i2)) = 0 Combine like terms: 11i + -21i = -10i (7 + -10i + -33i2) = 0 Solving 7 + -10i + -33i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -3i)(7 + 11i) = 0Subproblem 1
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 = 0.3333333333Subproblem 2
Set the factor '(7 + 11i)' equal to zero and attempt to solve: Simplifying 7 + 11i = 0 Solving 7 + 11i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 11i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 11i = 0 + -7 11i = 0 + -7 Combine like terms: 0 + -7 = -7 11i = -7 Divide each side by '11'. i = -0.6363636364 Simplifying i = -0.6363636364Solution
i = {0.3333333333, -0.6363636364}
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