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Simplifying (7 + 2i)(7 + 2i) = 0 Multiply (7 + 2i) * (7 + 2i) (7(7 + 2i) + 2i * (7 + 2i)) = 0 ((7 * 7 + 2i * 7) + 2i * (7 + 2i)) = 0 ((49 + 14i) + 2i * (7 + 2i)) = 0 (49 + 14i + (7 * 2i + 2i * 2i)) = 0 (49 + 14i + (14i + 4i2)) = 0 Combine like terms: 14i + 14i = 28i (49 + 28i + 4i2) = 0 Solving 49 + 28i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 2i)(7 + 2i) = 0Subproblem 1
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Subproblem 2
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Solution
i = {-3.5, -3.5}
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