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Simplifying (-1 + -3i)(-3 + -1i) = 0 Multiply (-1 + -3i) * (-3 + -1i) (-1(-3 + -1i) + -3i * (-3 + -1i)) = 0 ((-3 * -1 + -1i * -1) + -3i * (-3 + -1i)) = 0 ((3 + 1i) + -3i * (-3 + -1i)) = 0 (3 + 1i + (-3 * -3i + -1i * -3i)) = 0 (3 + 1i + (9i + 3i2)) = 0 Combine like terms: 1i + 9i = 10i (3 + 10i + 3i2) = 0 Solving 3 + 10i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + i)(1 + 3i) = 0Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Subproblem 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 = {-3, -0.3333333333}
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