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Simplifying (-5 + -2i)(-1 + -1i) = 0 Multiply (-5 + -2i) * (-1 + -1i) (-5(-1 + -1i) + -2i * (-1 + -1i)) = 0 ((-1 * -5 + -1i * -5) + -2i * (-1 + -1i)) = 0 ((5 + 5i) + -2i * (-1 + -1i)) = 0 (5 + 5i + (-1 * -2i + -1i * -2i)) = 0 (5 + 5i + (2i + 2i2)) = 0 Combine like terms: 5i + 2i = 7i (5 + 7i + 2i2) = 0 Solving 5 + 7i + 2i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 2i)(1 + i) = 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 '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {-2.5, -1}
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