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Simplifying (4 + 7i)(4 + 7i) = 0 Multiply (4 + 7i) * (4 + 7i) (4(4 + 7i) + 7i * (4 + 7i)) = 0 ((4 * 4 + 7i * 4) + 7i * (4 + 7i)) = 0 ((16 + 28i) + 7i * (4 + 7i)) = 0 (16 + 28i + (4 * 7i + 7i * 7i)) = 0 (16 + 28i + (28i + 49i2)) = 0 Combine like terms: 28i + 28i = 56i (16 + 56i + 49i2) = 0 Solving 16 + 56i + 49i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + 7i)(4 + 7i) = 0Subproblem 1
Set the factor '(4 + 7i)' equal to zero and attempt to solve: Simplifying 4 + 7i = 0 Solving 4 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7i = 0 + -4 7i = 0 + -4 Combine like terms: 0 + -4 = -4 7i = -4 Divide each side by '7'. i = -0.5714285714 Simplifying i = -0.5714285714Subproblem 2
Set the factor '(4 + 7i)' equal to zero and attempt to solve: Simplifying 4 + 7i = 0 Solving 4 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7i = 0 + -4 7i = 0 + -4 Combine like terms: 0 + -4 = -4 7i = -4 Divide each side by '7'. i = -0.5714285714 Simplifying i = -0.5714285714Solution
i = {-0.5714285714, -0.5714285714}
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