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