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Simplifying (-8 + 3i)(5 + i) = 0 Multiply (-8 + 3i) * (5 + i) (-8(5 + i) + 3i * (5 + i)) = 0 ((5 * -8 + i * -8) + 3i * (5 + i)) = 0 ((-40 + -8i) + 3i * (5 + i)) = 0 (-40 + -8i + (5 * 3i + i * 3i)) = 0 (-40 + -8i + (15i + 3i2)) = 0 Combine like terms: -8i + 15i = 7i (-40 + 7i + 3i2) = 0 Solving -40 + 7i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -1i)(8 + -3i) = 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 + -3i)' equal to zero and attempt to solve: Simplifying 8 + -3i = 0 Solving 8 + -3i = 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 + -3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3i = 0 + -8 -3i = 0 + -8 Combine like terms: 0 + -8 = -8 -3i = -8 Divide each side by '-3'. i = 2.666666667 Simplifying i = 2.666666667Solution
i = {-5, 2.666666667}
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