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Simplifying (-5 + 2i)(3 + -1i) = 0 Multiply (-5 + 2i) * (3 + -1i) (-5(3 + -1i) + 2i * (3 + -1i)) = 0 ((3 * -5 + -1i * -5) + 2i * (3 + -1i)) = 0 ((-15 + 5i) + 2i * (3 + -1i)) = 0 (-15 + 5i + (3 * 2i + -1i * 2i)) = 0 (-15 + 5i + (6i + -2i2)) = 0 Combine like terms: 5i + 6i = 11i (-15 + 11i + -2i2) = 0 Solving -15 + 11i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + i)(5 + -2i) = 0Subproblem 1
Set the factor '(-3 + i)' equal to zero and attempt to solve: Simplifying -3 + i = 0 Solving -3 + i = 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 + i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + i = 0 + 3 i = 0 + 3 Combine like terms: 0 + 3 = 3 i = 3 Simplifying i = 3Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Solution
i = {3, 2.5}
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