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Simplifying (7 + -1i)(4 + 2i) = 0 Multiply (7 + -1i) * (4 + 2i) (7(4 + 2i) + -1i * (4 + 2i)) = 0 ((4 * 7 + 2i * 7) + -1i * (4 + 2i)) = 0 ((28 + 14i) + -1i * (4 + 2i)) = 0 (28 + 14i + (4 * -1i + 2i * -1i)) = 0 (28 + 14i + (-4i + -2i2)) = 0 Combine like terms: 14i + -4i = 10i (28 + 10i + -2i2) = 0 Solving 28 + 10i + -2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 5i + -1i2) = 0 Factor a trinomial. 2((7 + -1i)(2 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -1i)' equal to zero and attempt to solve: Simplifying 7 + -1i = 0 Solving 7 + -1i = 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 + -1i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1i = 0 + -7 -1i = 0 + -7 Combine like terms: 0 + -7 = -7 -1i = -7 Divide each side by '-1'. 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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