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Simplifying (4 + -8i)(4 + -8i) = 0 Multiply (4 + -8i) * (4 + -8i) (4(4 + -8i) + -8i * (4 + -8i)) = 0 ((4 * 4 + -8i * 4) + -8i * (4 + -8i)) = 0 ((16 + -32i) + -8i * (4 + -8i)) = 0 (16 + -32i + (4 * -8i + -8i * -8i)) = 0 (16 + -32i + (-32i + 64i2)) = 0 Combine like terms: -32i + -32i = -64i (16 + -64i + 64i2) = 0 Solving 16 + -64i + 64i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '16'. 16(1 + -4i + 4i2) = 0 Factor a trinomial. 16((1 + -2i)(1 + -2i)) = 0 Ignore the factor 16.Subproblem 1
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 = 0.5Subproblem 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 = {0.5, 0.5}
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