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Simplifying (2 + 7i)(7 + -2i) = 0 Multiply (2 + 7i) * (7 + -2i) (2(7 + -2i) + 7i * (7 + -2i)) = 0 ((7 * 2 + -2i * 2) + 7i * (7 + -2i)) = 0 ((14 + -4i) + 7i * (7 + -2i)) = 0 (14 + -4i + (7 * 7i + -2i * 7i)) = 0 (14 + -4i + (49i + -14i2)) = 0 Combine like terms: -4i + 49i = 45i (14 + 45i + -14i2) = 0 Solving 14 + 45i + -14i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -2i)(2 + 7i) = 0Subproblem 1
Set the factor '(7 + -2i)' equal to zero and attempt to solve: Simplifying 7 + -2i = 0 Solving 7 + -2i = 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 + -2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2i = 0 + -7 -2i = 0 + -7 Combine like terms: 0 + -7 = -7 -2i = -7 Divide each side by '-2'. i = 3.5 Simplifying i = 3.5Subproblem 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 = {3.5, -0.2857142857}
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