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Simplifying (8 + -32i)(4 + -1i) = 0 Multiply (8 + -32i) * (4 + -1i) (8(4 + -1i) + -32i * (4 + -1i)) = 0 ((4 * 8 + -1i * 8) + -32i * (4 + -1i)) = 0 ((32 + -8i) + -32i * (4 + -1i)) = 0 (32 + -8i + (4 * -32i + -1i * -32i)) = 0 (32 + -8i + (-128i + 32i2)) = 0 Combine like terms: -8i + -128i = -136i (32 + -136i + 32i2) = 0 Solving 32 + -136i + 32i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8'. 8(4 + -17i + 4i2) = 0 Factor a trinomial. 8((1 + -4i)(4 + -1i)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -4i)' equal to zero and attempt to solve: Simplifying 1 + -4i = 0 Solving 1 + -4i = 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 + -4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i = 0 + -1 -4i = 0 + -1 Combine like terms: 0 + -1 = -1 -4i = -1 Divide each side by '-4'. i = 0.25 Simplifying i = 0.25Subproblem 2
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 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 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {0.25, 4}
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