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Simplifying (5 + -6i)(2 + 3i) = 0 Multiply (5 + -6i) * (2 + 3i) (5(2 + 3i) + -6i * (2 + 3i)) = 0 ((2 * 5 + 3i * 5) + -6i * (2 + 3i)) = 0 ((10 + 15i) + -6i * (2 + 3i)) = 0 (10 + 15i + (2 * -6i + 3i * -6i)) = 0 (10 + 15i + (-12i + -18i2)) = 0 Combine like terms: 15i + -12i = 3i (10 + 3i + -18i2) = 0 Solving 10 + 3i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -6i)(2 + 3i) = 0Subproblem 1
Set the factor '(5 + -6i)' equal to zero and attempt to solve: Simplifying 5 + -6i = 0 Solving 5 + -6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6i = 0 + -5 -6i = 0 + -5 Combine like terms: 0 + -5 = -5 -6i = -5 Divide each side by '-6'. i = 0.8333333333 Simplifying i = 0.8333333333Subproblem 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 = {0.8333333333, -0.6666666667}
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