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Simplifying (-1 + -1i)(5 + -3i) = 0 Multiply (-1 + -1i) * (5 + -3i) (-1(5 + -3i) + -1i * (5 + -3i)) = 0 ((5 * -1 + -3i * -1) + -1i * (5 + -3i)) = 0 ((-5 + 3i) + -1i * (5 + -3i)) = 0 (-5 + 3i + (5 * -1i + -3i * -1i)) = 0 (-5 + 3i + (-5i + 3i2)) = 0 Combine like terms: 3i + -5i = -2i (-5 + -2i + 3i2) = 0 Solving -5 + -2i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-1 + -1i)(5 + -3i) = 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 '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667Solution
i = {-1, 1.666666667}
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