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Simplifying (1 + -3i)(8 + 7i) = 0 Multiply (1 + -3i) * (8 + 7i) (1(8 + 7i) + -3i * (8 + 7i)) = 0 ((8 * 1 + 7i * 1) + -3i * (8 + 7i)) = 0 ((8 + 7i) + -3i * (8 + 7i)) = 0 (8 + 7i + (8 * -3i + 7i * -3i)) = 0 (8 + 7i + (-24i + -21i2)) = 0 Combine like terms: 7i + -24i = -17i (8 + -17i + -21i2) = 0 Solving 8 + -17i + -21i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -3i)(8 + 7i) = 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 '(8 + 7i)' equal to zero and attempt to solve: Simplifying 8 + 7i = 0 Solving 8 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7i = 0 + -8 7i = 0 + -8 Combine like terms: 0 + -8 = -8 7i = -8 Divide each side by '7'. i = -1.142857143 Simplifying i = -1.142857143Solution
i = {0.3333333333, -1.142857143}
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