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Simplifying (7 + -3i)(6 + i) = 0 Multiply (7 + -3i) * (6 + i) (7(6 + i) + -3i * (6 + i)) = 0 ((6 * 7 + i * 7) + -3i * (6 + i)) = 0 ((42 + 7i) + -3i * (6 + i)) = 0 (42 + 7i + (6 * -3i + i * -3i)) = 0 (42 + 7i + (-18i + -3i2)) = 0 Combine like terms: 7i + -18i = -11i (42 + -11i + -3i2) = 0 Solving 42 + -11i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -3i)(6 + i) = 0Subproblem 1
Set the factor '(7 + -3i)' equal to zero and attempt to solve: Simplifying 7 + -3i = 0 Solving 7 + -3i = 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 + -3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3i = 0 + -7 -3i = 0 + -7 Combine like terms: 0 + -7 = -7 -3i = -7 Divide each side by '-3'. i = 2.333333333 Simplifying i = 2.333333333Subproblem 2
Set the factor '(6 + i)' equal to zero and attempt to solve: Simplifying 6 + i = 0 Solving 6 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + i = 0 + -6 i = 0 + -6 Combine like terms: 0 + -6 = -6 i = -6 Simplifying i = -6Solution
i = {2.333333333, -6}
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