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Simplifying (1 + -9i)(3 + i) = 0 Multiply (1 + -9i) * (3 + i) (1(3 + i) + -9i * (3 + i)) = 0 ((3 * 1 + i * 1) + -9i * (3 + i)) = 0 ((3 + 1i) + -9i * (3 + i)) = 0 (3 + 1i + (3 * -9i + i * -9i)) = 0 (3 + 1i + (-27i + -9i2)) = 0 Combine like terms: 1i + -27i = -26i (3 + -26i + -9i2) = 0 Solving 3 + -26i + -9i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -9i)(3 + i) = 0Subproblem 1
Set the factor '(1 + -9i)' equal to zero and attempt to solve: Simplifying 1 + -9i = 0 Solving 1 + -9i = 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 + -9i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9i = 0 + -1 -9i = 0 + -1 Combine like terms: 0 + -1 = -1 -9i = -1 Divide each side by '-9'. i = 0.1111111111 Simplifying i = 0.1111111111Subproblem 2
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 = -3Solution
i = {0.1111111111, -3}
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