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Simplifying (3 + -5i)(7 + i) = 0 Multiply (3 + -5i) * (7 + i) (3(7 + i) + -5i * (7 + i)) = 0 ((7 * 3 + i * 3) + -5i * (7 + i)) = 0 ((21 + 3i) + -5i * (7 + i)) = 0 (21 + 3i + (7 * -5i + i * -5i)) = 0 (21 + 3i + (-35i + -5i2)) = 0 Combine like terms: 3i + -35i = -32i (21 + -32i + -5i2) = 0 Solving 21 + -32i + -5i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -5i)(7 + i) = 0Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Subproblem 2
Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 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 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7Solution
i = {0.6, -7}
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