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Simplifying (6 + -1i)(2 + i) = 0 Multiply (6 + -1i) * (2 + i) (6(2 + i) + -1i * (2 + i)) = 0 ((2 * 6 + i * 6) + -1i * (2 + i)) = 0 ((12 + 6i) + -1i * (2 + i)) = 0 (12 + 6i + (2 * -1i + i * -1i)) = 0 (12 + 6i + (-2i + -1i2)) = 0 Combine like terms: 6i + -2i = 4i (12 + 4i + -1i2) = 0 Solving 12 + 4i + -1i2 = 0 Solving for variable 'i'. Factor a trinomial. (6 + -1i)(2 + i) = 0Subproblem 1
Set the factor '(6 + -1i)' equal to zero and attempt to solve: Simplifying 6 + -1i = 0 Solving 6 + -1i = 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 + -1i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1i = 0 + -6 -1i = 0 + -6 Combine like terms: 0 + -6 = -6 -1i = -6 Divide each side by '-1'. i = 6 Simplifying i = 6Subproblem 2
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {6, -2}
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