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Simplifying (7 + 2i)(8 + -1i) = 0 Multiply (7 + 2i) * (8 + -1i) (7(8 + -1i) + 2i * (8 + -1i)) = 0 ((8 * 7 + -1i * 7) + 2i * (8 + -1i)) = 0 ((56 + -7i) + 2i * (8 + -1i)) = 0 (56 + -7i + (8 * 2i + -1i * 2i)) = 0 (56 + -7i + (16i + -2i2)) = 0 Combine like terms: -7i + 16i = 9i (56 + 9i + -2i2) = 0 Solving 56 + 9i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -1i)(7 + 2i) = 0Subproblem 1
Set the factor '(8 + -1i)' equal to zero and attempt to solve: Simplifying 8 + -1i = 0 Solving 8 + -1i = 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 + -1i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1i = 0 + -8 -1i = 0 + -8 Combine like terms: 0 + -8 = -8 -1i = -8 Divide each side by '-1'. i = 8 Simplifying i = 8Subproblem 2
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Solution
i = {8, -3.5}
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