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Simplifying (5 + 2i)(5 + 2i) = 0 Multiply (5 + 2i) * (5 + 2i) (5(5 + 2i) + 2i * (5 + 2i)) = 0 ((5 * 5 + 2i * 5) + 2i * (5 + 2i)) = 0 ((25 + 10i) + 2i * (5 + 2i)) = 0 (25 + 10i + (5 * 2i + 2i * 2i)) = 0 (25 + 10i + (10i + 4i2)) = 0 Combine like terms: 10i + 10i = 20i (25 + 20i + 4i2) = 0 Solving 25 + 20i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 2i)(5 + 2i) = 0Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve: Simplifying 5 + 2i = 0 Solving 5 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5Subproblem 2
Set the factor '(5 + 2i)' equal to zero and attempt to solve: Simplifying 5 + 2i = 0 Solving 5 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5Solution
i = {-2.5, -2.5}
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