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Simplifying (2 + -1i)(-5 + 3i) = 0 Multiply (2 + -1i) * (-5 + 3i) (2(-5 + 3i) + -1i * (-5 + 3i)) = 0 ((-5 * 2 + 3i * 2) + -1i * (-5 + 3i)) = 0 ((-10 + 6i) + -1i * (-5 + 3i)) = 0 (-10 + 6i + (-5 * -1i + 3i * -1i)) = 0 (-10 + 6i + (5i + -3i2)) = 0 Combine like terms: 6i + 5i = 11i (-10 + 11i + -3i2) = 0 Solving -10 + 11i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + i)(5 + -3i) = 0Subproblem 1
Set the factor '(-2 + i)' equal to zero and attempt to solve: Simplifying -2 + i = 0 Solving -2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + i = 0 + 2 i = 0 + 2 Combine like terms: 0 + 2 = 2 i = 2 Simplifying i = 2Subproblem 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 = {2, 1.666666667}
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