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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. (3 + -2i)(8 + 5i) = 0Subproblem 1
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 = 1.5Subproblem 2
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 = -1.6Solution
i = {1.5, -1.6}
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