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Simplifying (3 + i)(-4 + 3i) = 0 Multiply (3 + i) * (-4 + 3i) (3(-4 + 3i) + i(-4 + 3i)) = 0 ((-4 * 3 + 3i * 3) + i(-4 + 3i)) = 0 ((-12 + 9i) + i(-4 + 3i)) = 0 (-12 + 9i + (-4 * i + 3i * i)) = 0 (-12 + 9i + (-4i + 3i2)) = 0 Combine like terms: 9i + -4i = 5i (-12 + 5i + 3i2) = 0 Solving -12 + 5i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -1i)(4 + -3i) = 0Subproblem 1
Set the factor '(-3 + -1i)' equal to zero and attempt to solve: Simplifying -3 + -1i = 0 Solving -3 + -1i = 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 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3Subproblem 2
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 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 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Solution
i = {-3, 1.333333333}
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