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Simplifying (6 + -1i)(-2 + -1i) = 0 Multiply (6 + -1i) * (-2 + -1i) (6(-2 + -1i) + -1i * (-2 + -1i)) = 0 ((-2 * 6 + -1i * 6) + -1i * (-2 + -1i)) = 0 ((-12 + -6i) + -1i * (-2 + -1i)) = 0 (-12 + -6i + (-2 * -1i + -1i * -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. (-2 + -1i)(6 + -1i) = 0Subproblem 1
Set the factor '(-2 + -1i)' equal to zero and attempt to solve: Simplifying -2 + -1i = 0 Solving -2 + -1i = 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 + -1i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1i = 0 + 2 -1i = 0 + 2 Combine like terms: 0 + 2 = 2 -1i = 2 Divide each side by '-1'. i = -2 Simplifying i = -2Subproblem 2
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 = 6Solution
i = {-2, 6}
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