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Simplifying (-1 + 2i)(11 + -1i) = 0 Multiply (-1 + 2i) * (11 + -1i) (-1(11 + -1i) + 2i * (11 + -1i)) = 0 ((11 * -1 + -1i * -1) + 2i * (11 + -1i)) = 0 ((-11 + 1i) + 2i * (11 + -1i)) = 0 (-11 + 1i + (11 * 2i + -1i * 2i)) = 0 (-11 + 1i + (22i + -2i2)) = 0 Combine like terms: 1i + 22i = 23i (-11 + 23i + -2i2) = 0 Solving -11 + 23i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (-11 + i)(1 + -2i) = 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 '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Solution
i = {11, 0.5}
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