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Simplifying (4 + 5i)(4 + 5i) = 0 Multiply (4 + 5i) * (4 + 5i) (4(4 + 5i) + 5i * (4 + 5i)) = 0 ((4 * 4 + 5i * 4) + 5i * (4 + 5i)) = 0 ((16 + 20i) + 5i * (4 + 5i)) = 0 (16 + 20i + (4 * 5i + 5i * 5i)) = 0 (16 + 20i + (20i + 25i2)) = 0 Combine like terms: 20i + 20i = 40i (16 + 40i + 25i2) = 0 Solving 16 + 40i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + 5i)(4 + 5i) = 0Subproblem 1
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Subproblem 2
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Solution
i = {-0.8, -0.8}
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