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Simplifying (3 + -2i)(7 + 6i) = 0 Multiply (3 + -2i) * (7 + 6i) (3(7 + 6i) + -2i * (7 + 6i)) = 0 ((7 * 3 + 6i * 3) + -2i * (7 + 6i)) = 0 ((21 + 18i) + -2i * (7 + 6i)) = 0 (21 + 18i + (7 * -2i + 6i * -2i)) = 0 (21 + 18i + (-14i + -12i2)) = 0 Combine like terms: 18i + -14i = 4i (21 + 4i + -12i2) = 0 Solving 21 + 4i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -2i)(7 + 6i) = 0Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Subproblem 2
Set the factor '(7 + 6i)' equal to zero and attempt to solve: Simplifying 7 + 6i = 0 Solving 7 + 6i = 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 + 6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6i = 0 + -7 6i = 0 + -7 Combine like terms: 0 + -7 = -7 6i = -7 Divide each side by '6'. i = -1.166666667 Simplifying i = -1.166666667Solution
i = {1.5, -1.166666667}
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