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Simplifying (5 + 2i)(2 + 2i) = 0 Multiply (5 + 2i) * (2 + 2i) (5(2 + 2i) + 2i * (2 + 2i)) = 0 ((2 * 5 + 2i * 5) + 2i * (2 + 2i)) = 0 ((10 + 10i) + 2i * (2 + 2i)) = 0 (10 + 10i + (2 * 2i + 2i * 2i)) = 0 (10 + 10i + (4i + 4i2)) = 0 Combine like terms: 10i + 4i = 14i (10 + 14i + 4i2) = 0 Solving 10 + 14i + 4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 7i + 2i2) = 0 Factor a trinomial. 2((5 + 2i)(1 + i)) = 0 Ignore the factor 2.Subproblem 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 '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {-2.5, -1}
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