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Simplifying (2 + -3i)(7 + -6i) = 0 Multiply (2 + -3i) * (7 + -6i) (2(7 + -6i) + -3i * (7 + -6i)) = 0 ((7 * 2 + -6i * 2) + -3i * (7 + -6i)) = 0 ((14 + -12i) + -3i * (7 + -6i)) = 0 (14 + -12i + (7 * -3i + -6i * -3i)) = 0 (14 + -12i + (-21i + 18i2)) = 0 Combine like terms: -12i + -21i = -33i (14 + -33i + 18i2) = 0 Solving 14 + -33i + 18i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(7 + -6i) = 0Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 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 = {0.6666666667, 1.166666667}
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