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Simplifying (8 + -7i)(4 + i) = 0 Multiply (8 + -7i) * (4 + i) (8(4 + i) + -7i * (4 + i)) = 0 ((4 * 8 + i * 8) + -7i * (4 + i)) = 0 ((32 + 8i) + -7i * (4 + i)) = 0 (32 + 8i + (4 * -7i + i * -7i)) = 0 (32 + 8i + (-28i + -7i2)) = 0 Combine like terms: 8i + -28i = -20i (32 + -20i + -7i2) = 0 Solving 32 + -20i + -7i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -7i)(4 + i) = 0Subproblem 1
Set the factor '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Subproblem 2
Set the factor '(4 + i)' equal to zero and attempt to solve: Simplifying 4 + i = 0 Solving 4 + i = 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 + i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + i = 0 + -4 i = 0 + -4 Combine like terms: 0 + -4 = -4 i = -4 Simplifying i = -4Solution
i = {1.142857143, -4}
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