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Simplifying (-8 + 7i)(5 + i) = 0 Multiply (-8 + 7i) * (5 + i) (-8(5 + i) + 7i * (5 + i)) = 0 ((5 * -8 + i * -8) + 7i * (5 + i)) = 0 ((-40 + -8i) + 7i * (5 + i)) = 0 (-40 + -8i + (5 * 7i + i * 7i)) = 0 (-40 + -8i + (35i + 7i2)) = 0 Combine like terms: -8i + 35i = 27i (-40 + 27i + 7i2) = 0 Solving -40 + 27i + 7i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -1i)(8 + -7i) = 0Subproblem 1
Set the factor '(-5 + -1i)' equal to zero and attempt to solve: Simplifying -5 + -1i = 0 Solving -5 + -1i = 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 + -1i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1i = 0 + 5 -1i = 0 + 5 Combine like terms: 0 + 5 = 5 -1i = 5 Divide each side by '-1'. i = -5 Simplifying i = -5Subproblem 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 = {-5, 1.142857143}
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