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Simplifying (8 + -3i)(6 + 5i) = 0 Multiply (8 + -3i) * (6 + 5i) (8(6 + 5i) + -3i * (6 + 5i)) = 0 ((6 * 8 + 5i * 8) + -3i * (6 + 5i)) = 0 ((48 + 40i) + -3i * (6 + 5i)) = 0 (48 + 40i + (6 * -3i + 5i * -3i)) = 0 (48 + 40i + (-18i + -15i2)) = 0 Combine like terms: 40i + -18i = 22i (48 + 22i + -15i2) = 0 Solving 48 + 22i + -15i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -3i)(6 + 5i) = 0Subproblem 1
Set the factor '(8 + -3i)' equal to zero and attempt to solve: Simplifying 8 + -3i = 0 Solving 8 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3i = 0 + -8 -3i = 0 + -8 Combine like terms: 0 + -8 = -8 -3i = -8 Divide each side by '-3'. i = 2.666666667 Simplifying i = 2.666666667Subproblem 2
Set the factor '(6 + 5i)' equal to zero and attempt to solve: Simplifying 6 + 5i = 0 Solving 6 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5i = 0 + -6 5i = 0 + -6 Combine like terms: 0 + -6 = -6 5i = -6 Divide each side by '5'. i = -1.2 Simplifying i = -1.2Solution
i = {2.666666667, -1.2}
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