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Simplifying (10 + i)(5 + -8i) = 0 Multiply (10 + i) * (5 + -8i) (10(5 + -8i) + i(5 + -8i)) = 0 ((5 * 10 + -8i * 10) + i(5 + -8i)) = 0 ((50 + -80i) + i(5 + -8i)) = 0 (50 + -80i + (5 * i + -8i * i)) = 0 (50 + -80i + (5i + -8i2)) = 0 Combine like terms: -80i + 5i = -75i (50 + -75i + -8i2) = 0 Solving 50 + -75i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -8i)(10 + i) = 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 '(10 + i)' equal to zero and attempt to solve: Simplifying 10 + i = 0 Solving 10 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + i = 0 + -10 Combine like terms: 10 + -10 = 0 0 + i = 0 + -10 i = 0 + -10 Combine like terms: 0 + -10 = -10 i = -10 Simplifying i = -10Solution
i = {0.625, -10}
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