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Simplifying (-2 + -2i)(-8 + -8i) = 0 Multiply (-2 + -2i) * (-8 + -8i) (-2(-8 + -8i) + -2i * (-8 + -8i)) = 0 ((-8 * -2 + -8i * -2) + -2i * (-8 + -8i)) = 0 ((16 + 16i) + -2i * (-8 + -8i)) = 0 (16 + 16i + (-8 * -2i + -8i * -2i)) = 0 (16 + 16i + (16i + 16i2)) = 0 Combine like terms: 16i + 16i = 32i (16 + 32i + 16i2) = 0 Solving 16 + 32i + 16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '16'. 16(1 + 2i + i2) = 0 Factor a trinomial. 16((1 + i)(1 + i)) = 0 Ignore the factor 16.Subproblem 1
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 = -1Subproblem 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 = {-1, -1}
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