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Simplifying (4 + 2i)(7 + i) = 0 Multiply (4 + 2i) * (7 + i) (4(7 + i) + 2i * (7 + i)) = 0 ((7 * 4 + i * 4) + 2i * (7 + i)) = 0 ((28 + 4i) + 2i * (7 + i)) = 0 (28 + 4i + (7 * 2i + i * 2i)) = 0 (28 + 4i + (14i + 2i2)) = 0 Combine like terms: 4i + 14i = 18i (28 + 18i + 2i2) = 0 Solving 28 + 18i + 2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 9i + i2) = 0 Factor a trinomial. 2((7 + i)(2 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7Subproblem 2
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {-7, -2}
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