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Simplifying (2 + 5i)(2 + 5i) = 0 Multiply (2 + 5i) * (2 + 5i) (2(2 + 5i) + 5i * (2 + 5i)) = 0 ((2 * 2 + 5i * 2) + 5i * (2 + 5i)) = 0 ((4 + 10i) + 5i * (2 + 5i)) = 0 (4 + 10i + (2 * 5i + 5i * 5i)) = 0 (4 + 10i + (10i + 25i2)) = 0 Combine like terms: 10i + 10i = 20i (4 + 20i + 25i2) = 0 Solving 4 + 20i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + 5i)(2 + 5i) = 0Subproblem 1
Set the factor '(2 + 5i)' equal to zero and attempt to solve: Simplifying 2 + 5i = 0 Solving 2 + 5i = 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 + 5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5i = 0 + -2 5i = 0 + -2 Combine like terms: 0 + -2 = -2 5i = -2 Divide each side by '5'. i = -0.4 Simplifying i = -0.4Subproblem 2
Set the factor '(2 + 5i)' equal to zero and attempt to solve: Simplifying 2 + 5i = 0 Solving 2 + 5i = 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 + 5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5i = 0 + -2 5i = 0 + -2 Combine like terms: 0 + -2 = -2 5i = -2 Divide each side by '5'. i = -0.4 Simplifying i = -0.4Solution
i = {-0.4, -0.4}
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