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Simplifying (5 + 8j)(4 + -2j) = 0 Multiply (5 + 8j) * (4 + -2j) (5(4 + -2j) + 8j * (4 + -2j)) = 0 ((4 * 5 + -2j * 5) + 8j * (4 + -2j)) = 0 ((20 + -10j) + 8j * (4 + -2j)) = 0 (20 + -10j + (4 * 8j + -2j * 8j)) = 0 (20 + -10j + (32j + -16j2)) = 0 Combine like terms: -10j + 32j = 22j (20 + 22j + -16j2) = 0 Solving 20 + 22j + -16j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 11j + -8j2) = 0 Factor a trinomial. 2((2 + -1j)(5 + 8j)) = 0 Ignore the factor 2.Subproblem 1
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 = 2Subproblem 2
Set the factor '(5 + 8j)' equal to zero and attempt to solve: Simplifying 5 + 8j = 0 Solving 5 + 8j = 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 + 8j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8j = 0 + -5 8j = 0 + -5 Combine like terms: 0 + -5 = -5 8j = -5 Divide each side by '8'. j = -0.625 Simplifying j = -0.625Solution
j = {2, -0.625}
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