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Simplifying (8j + 3)(j + -2) = 0 Reorder the terms: (3 + 8j)(j + -2) = 0 Reorder the terms: (3 + 8j)(-2 + j) = 0 Multiply (3 + 8j) * (-2 + j) (3(-2 + j) + 8j * (-2 + j)) = 0 ((-2 * 3 + j * 3) + 8j * (-2 + j)) = 0 ((-6 + 3j) + 8j * (-2 + j)) = 0 (-6 + 3j + (-2 * 8j + j * 8j)) = 0 (-6 + 3j + (-16j + 8j2)) = 0 Combine like terms: 3j + -16j = -13j (-6 + -13j + 8j2) = 0 Solving -6 + -13j + 8j2 = 0 Solving for variable 'j'. Factor a trinomial. (-3 + -8j)(2 + -1j) = 0Subproblem 1
Set the factor '(-3 + -8j)' equal to zero and attempt to solve: Simplifying -3 + -8j = 0 Solving -3 + -8j = 0 Move all terms containing j to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -8j = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8j = 0 + 3 -8j = 0 + 3 Combine like terms: 0 + 3 = 3 -8j = 3 Divide each side by '-8'. j = -0.375 Simplifying j = -0.375Subproblem 2
Set the factor '(2 + -1j)' equal to zero and attempt to solve: Simplifying 2 + -1j = 0 Solving 2 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1j = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1j = 0 + -2 -1j = 0 + -2 Combine like terms: 0 + -2 = -2 -1j = -2 Divide each side by '-1'. j = 2 Simplifying j = 2Solution
j = {-0.375, 2}
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