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Simplifying (7 + 5i)(7 + 5i) = 0 Multiply (7 + 5i) * (7 + 5i) (7(7 + 5i) + 5i * (7 + 5i)) = 0 ((7 * 7 + 5i * 7) + 5i * (7 + 5i)) = 0 ((49 + 35i) + 5i * (7 + 5i)) = 0 (49 + 35i + (7 * 5i + 5i * 5i)) = 0 (49 + 35i + (35i + 25i2)) = 0 Combine like terms: 35i + 35i = 70i (49 + 70i + 25i2) = 0 Solving 49 + 70i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 5i)(7 + 5i) = 0Subproblem 1
Set the factor '(7 + 5i)' equal to zero and attempt to solve: Simplifying 7 + 5i = 0 Solving 7 + 5i = 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 + 5i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5i = 0 + -7 5i = 0 + -7 Combine like terms: 0 + -7 = -7 5i = -7 Divide each side by '5'. i = -1.4 Simplifying i = -1.4Subproblem 2
Set the factor '(7 + 5i)' equal to zero and attempt to solve: Simplifying 7 + 5i = 0 Solving 7 + 5i = 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 + 5i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5i = 0 + -7 5i = 0 + -7 Combine like terms: 0 + -7 = -7 5i = -7 Divide each side by '5'. i = -1.4 Simplifying i = -1.4Solution
i = {-1.4, -1.4}
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