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Simplifying (5 + -1i)(-11 + i) = 0 Multiply (5 + -1i) * (-11 + i) (5(-11 + i) + -1i * (-11 + i)) = 0 ((-11 * 5 + i * 5) + -1i * (-11 + i)) = 0 ((-55 + 5i) + -1i * (-11 + i)) = 0 (-55 + 5i + (-11 * -1i + i * -1i)) = 0 (-55 + 5i + (11i + -1i2)) = 0 Combine like terms: 5i + 11i = 16i (-55 + 16i + -1i2) = 0 Solving -55 + 16i + -1i2 = 0 Solving for variable 'i'. Factor a trinomial. (-11 + i)(5 + -1i) = 0Subproblem 1
Set the factor '(-11 + i)' equal to zero and attempt to solve: Simplifying -11 + i = 0 Solving -11 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + i = 0 + 11 Combine like terms: -11 + 11 = 0 0 + i = 0 + 11 i = 0 + 11 Combine like terms: 0 + 11 = 11 i = 11 Simplifying i = 11Subproblem 2
Set the factor '(5 + -1i)' equal to zero and attempt to solve: Simplifying 5 + -1i = 0 Solving 5 + -1i = 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 + -1i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i = 0 + -5 -1i = 0 + -5 Combine like terms: 0 + -5 = -5 -1i = -5 Divide each side by '-1'. i = 5 Simplifying i = 5Solution
i = {11, 5}
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