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Simplifying (7 + 4i)(7 + 4i) = 0 Multiply (7 + 4i) * (7 + 4i) (7(7 + 4i) + 4i * (7 + 4i)) = 0 ((7 * 7 + 4i * 7) + 4i * (7 + 4i)) = 0 ((49 + 28i) + 4i * (7 + 4i)) = 0 (49 + 28i + (7 * 4i + 4i * 4i)) = 0 (49 + 28i + (28i + 16i2)) = 0 Combine like terms: 28i + 28i = 56i (49 + 56i + 16i2) = 0 Solving 49 + 56i + 16i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 4i)(7 + 4i) = 0Subproblem 1
Set the factor '(7 + 4i)' equal to zero and attempt to solve: Simplifying 7 + 4i = 0 Solving 7 + 4i = 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 + 4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4i = 0 + -7 4i = 0 + -7 Combine like terms: 0 + -7 = -7 4i = -7 Divide each side by '4'. i = -1.75 Simplifying i = -1.75Subproblem 2
Set the factor '(7 + 4i)' equal to zero and attempt to solve: Simplifying 7 + 4i = 0 Solving 7 + 4i = 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 + 4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4i = 0 + -7 4i = 0 + -7 Combine like terms: 0 + -7 = -7 4i = -7 Divide each side by '4'. i = -1.75 Simplifying i = -1.75Solution
i = {-1.75, -1.75}
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