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Simplifying (-3 + i)(-8 + 7i) = 0 Multiply (-3 + i) * (-8 + 7i) (-3(-8 + 7i) + i(-8 + 7i)) = 0 ((-8 * -3 + 7i * -3) + i(-8 + 7i)) = 0 ((24 + -21i) + i(-8 + 7i)) = 0 (24 + -21i + (-8 * i + 7i * i)) = 0 (24 + -21i + (-8i + 7i2)) = 0 Combine like terms: -21i + -8i = -29i (24 + -29i + 7i2) = 0 Solving 24 + -29i + 7i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -7i)(3 + -1i) = 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 '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Solution
i = {1.142857143, 3}
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