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Simplifying (2 + 4i)(4 + -1i) = 0 Multiply (2 + 4i) * (4 + -1i) (2(4 + -1i) + 4i * (4 + -1i)) = 0 ((4 * 2 + -1i * 2) + 4i * (4 + -1i)) = 0 ((8 + -2i) + 4i * (4 + -1i)) = 0 (8 + -2i + (4 * 4i + -1i * 4i)) = 0 (8 + -2i + (16i + -4i2)) = 0 Combine like terms: -2i + 16i = 14i (8 + 14i + -4i2) = 0 Solving 8 + 14i + -4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 7i + -2i2) = 0 Factor a trinomial. 2((4 + -1i)(1 + 2i)) = 0 Ignore the factor 2.Subproblem 1
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 = 4Subproblem 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 = {4, -0.5}
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