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Simplifying (4 + 3j)(5 + -2j) = 0 Multiply (4 + 3j) * (5 + -2j) (4(5 + -2j) + 3j * (5 + -2j)) = 0 ((5 * 4 + -2j * 4) + 3j * (5 + -2j)) = 0 ((20 + -8j) + 3j * (5 + -2j)) = 0 (20 + -8j + (5 * 3j + -2j * 3j)) = 0 (20 + -8j + (15j + -6j2)) = 0 Combine like terms: -8j + 15j = 7j (20 + 7j + -6j2) = 0 Solving 20 + 7j + -6j2 = 0 Solving for variable 'j'. Factor a trinomial. (5 + -2j)(4 + 3j) = 0Subproblem 1
Set the factor '(5 + -2j)' equal to zero and attempt to solve: Simplifying 5 + -2j = 0 Solving 5 + -2j = 0 Move all terms containing j to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2j = 0 + -5 -2j = 0 + -5 Combine like terms: 0 + -5 = -5 -2j = -5 Divide each side by '-2'. j = 2.5 Simplifying j = 2.5Subproblem 2
Set the factor '(4 + 3j)' equal to zero and attempt to solve: Simplifying 4 + 3j = 0 Solving 4 + 3j = 0 Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3j = 0 + -4 3j = 0 + -4 Combine like terms: 0 + -4 = -4 3j = -4 Divide each side by '3'. j = -1.333333333 Simplifying j = -1.333333333Solution
j = {2.5, -1.333333333}
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