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Simplifying (7 + 3i)(6 + -1i) = 0 Multiply (7 + 3i) * (6 + -1i) (7(6 + -1i) + 3i * (6 + -1i)) = 0 ((6 * 7 + -1i * 7) + 3i * (6 + -1i)) = 0 ((42 + -7i) + 3i * (6 + -1i)) = 0 (42 + -7i + (6 * 3i + -1i * 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. (6 + -1i)(7 + 3i) = 0Subproblem 1
Set the factor '(6 + -1i)' equal to zero and attempt to solve: Simplifying 6 + -1i = 0 Solving 6 + -1i = 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 + -1i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1i = 0 + -6 -1i = 0 + -6 Combine like terms: 0 + -6 = -6 -1i = -6 Divide each side by '-1'. i = 6 Simplifying i = 6Subproblem 2
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 = -2.333333333Solution
i = {6, -2.333333333}
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