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Simplifying (5 + -8i)(5 + -8i) = 0 Multiply (5 + -8i) * (5 + -8i) (5(5 + -8i) + -8i * (5 + -8i)) = 0 ((5 * 5 + -8i * 5) + -8i * (5 + -8i)) = 0 ((25 + -40i) + -8i * (5 + -8i)) = 0 (25 + -40i + (5 * -8i + -8i * -8i)) = 0 (25 + -40i + (-40i + 64i2)) = 0 Combine like terms: -40i + -40i = -80i (25 + -80i + 64i2) = 0 Solving 25 + -80i + 64i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -8i)(5 + -8i) = 0Subproblem 1
Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625Subproblem 2
Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625Solution
i = {0.625, 0.625}
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