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Simplifying (3 + 2i)(8 + -5i) = 0 Multiply (3 + 2i) * (8 + -5i) (3(8 + -5i) + 2i * (8 + -5i)) = 0 ((8 * 3 + -5i * 3) + 2i * (8 + -5i)) = 0 ((24 + -15i) + 2i * (8 + -5i)) = 0 (24 + -15i + (8 * 2i + -5i * 2i)) = 0 (24 + -15i + (16i + -10i2)) = 0 Combine like terms: -15i + 16i = 1i (24 + 1i + -10i2) = 0 Solving 24 + 1i + -10i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -5i)(3 + 2i) = 0Subproblem 1
Set the factor '(8 + -5i)' equal to zero and attempt to solve: Simplifying 8 + -5i = 0 Solving 8 + -5i = 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 + -5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5i = 0 + -8 -5i = 0 + -8 Combine like terms: 0 + -8 = -8 -5i = -8 Divide each side by '-5'. i = 1.6 Simplifying i = 1.6Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {1.6, -1.5}
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