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Simplifying (7 + -6i)(-2 + 3i) = 0 Multiply (7 + -6i) * (-2 + 3i) (7(-2 + 3i) + -6i * (-2 + 3i)) = 0 ((-2 * 7 + 3i * 7) + -6i * (-2 + 3i)) = 0 ((-14 + 21i) + -6i * (-2 + 3i)) = 0 (-14 + 21i + (-2 * -6i + 3i * -6i)) = 0 (-14 + 21i + (12i + -18i2)) = 0 Combine like terms: 21i + 12i = 33i (-14 + 33i + -18i2) = 0 Solving -14 + 33i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + 6i)(2 + -3i) = 0Subproblem 1
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 = 1.166666667Subproblem 2
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 = 0.6666666667Solution
i = {1.166666667, 0.6666666667}
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