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Simplifying i(2 + 7i)(2 + -7i) = 0 Multiply (2 + 7i) * (2 + -7i) i(2(2 + -7i) + 7i * (2 + -7i)) = 0 i((2 * 2 + -7i * 2) + 7i * (2 + -7i)) = 0 i((4 + -14i) + 7i * (2 + -7i)) = 0 i(4 + -14i + (2 * 7i + -7i * 7i)) = 0 i(4 + -14i + (14i + -49i2)) = 0 Combine like terms: -14i + 14i = 0 i(4 + 0 + -49i2) = 0 i(4 + -49i2) = 0 (4 * i + -49i2 * i) = 0 (4i + -49i3) = 0 Solving 4i + -49i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'i'. i(4 + -49i2) = 0 Factor a difference between two squares. i((2 + 7i)(2 + -7i)) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 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 = -0.2857142857Subproblem 3
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 = {0, -0.2857142857, 0.2857142857}
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