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Simplifying (2 + 3i)(5 + -3i) = 0 Multiply (2 + 3i) * (5 + -3i) (2(5 + -3i) + 3i * (5 + -3i)) = 0 ((5 * 2 + -3i * 2) + 3i * (5 + -3i)) = 0 ((10 + -6i) + 3i * (5 + -3i)) = 0 (10 + -6i + (5 * 3i + -3i * 3i)) = 0 (10 + -6i + (15i + -9i2)) = 0 Combine like terms: -6i + 15i = 9i (10 + 9i + -9i2) = 0 Solving 10 + 9i + -9i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -3i)(2 + 3i) = 0Subproblem 1
Set the factor '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667Subproblem 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 = {1.666666667, -0.6666666667}
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