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Simplifying (-3 + 2i)(5 + -1i) = 0 Multiply (-3 + 2i) * (5 + -1i) (-3(5 + -1i) + 2i * (5 + -1i)) = 0 ((5 * -3 + -1i * -3) + 2i * (5 + -1i)) = 0 ((-15 + 3i) + 2i * (5 + -1i)) = 0 (-15 + 3i + (5 * 2i + -1i * 2i)) = 0 (-15 + 3i + (10i + -2i2)) = 0 Combine like terms: 3i + 10i = 13i (-15 + 13i + -2i2) = 0 Solving -15 + 13i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + i)(3 + -2i) = 0Subproblem 1
Set the factor '(-5 + i)' equal to zero and attempt to solve: Simplifying -5 + i = 0 Solving -5 + i = 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 + i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + i = 0 + 5 i = 0 + 5 Combine like terms: 0 + 5 = 5 i = 5 Simplifying i = 5Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 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 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {5, 1.5}
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