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Simplifying (4 + 11i)(-3 + 5i) = 0 Multiply (4 + 11i) * (-3 + 5i) (4(-3 + 5i) + 11i * (-3 + 5i)) = 0 ((-3 * 4 + 5i * 4) + 11i * (-3 + 5i)) = 0 ((-12 + 20i) + 11i * (-3 + 5i)) = 0 (-12 + 20i + (-3 * 11i + 5i * 11i)) = 0 (-12 + 20i + (-33i + 55i2)) = 0 Combine like terms: 20i + -33i = -13i (-12 + -13i + 55i2) = 0 Solving -12 + -13i + 55i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -11i)(3 + -5i) = 0Subproblem 1
Set the factor '(-4 + -11i)' equal to zero and attempt to solve: Simplifying -4 + -11i = 0 Solving -4 + -11i = 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 + -11i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -11i = 0 + 4 -11i = 0 + 4 Combine like terms: 0 + 4 = 4 -11i = 4 Divide each side by '-11'. i = -0.3636363636 Simplifying i = -0.3636363636Subproblem 2
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 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 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Solution
i = {-0.3636363636, 0.6}
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