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Simplifying (5 + -2i)(8 + -1i) = 0 Multiply (5 + -2i) * (8 + -1i) (5(8 + -1i) + -2i * (8 + -1i)) = 0 ((8 * 5 + -1i * 5) + -2i * (8 + -1i)) = 0 ((40 + -5i) + -2i * (8 + -1i)) = 0 (40 + -5i + (8 * -2i + -1i * -2i)) = 0 (40 + -5i + (-16i + 2i2)) = 0 Combine like terms: -5i + -16i = -21i (40 + -21i + 2i2) = 0 Solving 40 + -21i + 2i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -2i)(8 + -1i) = 0Subproblem 1
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Subproblem 2
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 = 8Solution
i = {2.5, 8}
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