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Simplifying (8 + 2i)(8 + 2i) = 0 Multiply (8 + 2i) * (8 + 2i) (8(8 + 2i) + 2i * (8 + 2i)) = 0 ((8 * 8 + 2i * 8) + 2i * (8 + 2i)) = 0 ((64 + 16i) + 2i * (8 + 2i)) = 0 (64 + 16i + (8 * 2i + 2i * 2i)) = 0 (64 + 16i + (16i + 4i2)) = 0 Combine like terms: 16i + 16i = 32i (64 + 32i + 4i2) = 0 Solving 64 + 32i + 4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + 8i + i2) = 0 Factor a trinomial. 4((4 + i)(4 + i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Subproblem 2
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Solution
i = {-4, -4}
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