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Simplifying (3 + -2i)(-4 + i) = 0 Multiply (3 + -2i) * (-4 + i) (3(-4 + i) + -2i * (-4 + i)) = 0 ((-4 * 3 + i * 3) + -2i * (-4 + i)) = 0 ((-12 + 3i) + -2i * (-4 + i)) = 0 (-12 + 3i + (-4 * -2i + i * -2i)) = 0 (-12 + 3i + (8i + -2i2)) = 0 Combine like terms: 3i + 8i = 11i (-12 + 11i + -2i2) = 0 Solving -12 + 11i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + i)(3 + -2i) = 0Subproblem 1
Set the factor '(-4 + i)' equal to zero and attempt to solve: Simplifying -4 + i = 0 Solving -4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + i = 0 + 4 i = 0 + 4 Combine like terms: 0 + 4 = 4 i = 4 Simplifying i = 4Subproblem 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 = {4, 1.5}
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