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Simplifying (4 + -2i)(2 + 7i) = 0 Multiply (4 + -2i) * (2 + 7i) (4(2 + 7i) + -2i * (2 + 7i)) = 0 ((2 * 4 + 7i * 4) + -2i * (2 + 7i)) = 0 ((8 + 28i) + -2i * (2 + 7i)) = 0 (8 + 28i + (2 * -2i + 7i * -2i)) = 0 (8 + 28i + (-4i + -14i2)) = 0 Combine like terms: 28i + -4i = 24i (8 + 24i + -14i2) = 0 Solving 8 + 24i + -14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 12i + -7i2) = 0 Factor a trinomial. 2((2 + -1i)(2 + 7i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve: Simplifying 2 + 7i = 0 Solving 2 + 7i = 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 + 7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7i = 0 + -2 7i = 0 + -2 Combine like terms: 0 + -2 = -2 7i = -2 Divide each side by '7'. i = -0.2857142857 Simplifying i = -0.2857142857Solution
i = {2, -0.2857142857}
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