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Simplifying (6 + -2j)(5 + 3j) = 0 Multiply (6 + -2j) * (5 + 3j) (6(5 + 3j) + -2j * (5 + 3j)) = 0 ((5 * 6 + 3j * 6) + -2j * (5 + 3j)) = 0 ((30 + 18j) + -2j * (5 + 3j)) = 0 (30 + 18j + (5 * -2j + 3j * -2j)) = 0 (30 + 18j + (-10j + -6j2)) = 0 Combine like terms: 18j + -10j = 8j (30 + 8j + -6j2) = 0 Solving 30 + 8j + -6j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 4j + -3j2) = 0 Factor a trinomial. 2((3 + -1j)(5 + 3j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1j)' equal to zero and attempt to solve: Simplifying 3 + -1j = 0 Solving 3 + -1j = 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 + -1j = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1j = 0 + -3 -1j = 0 + -3 Combine like terms: 0 + -3 = -3 -1j = -3 Divide each side by '-1'. j = 3 Simplifying j = 3Subproblem 2
Set the factor '(5 + 3j)' equal to zero and attempt to solve: Simplifying 5 + 3j = 0 Solving 5 + 3j = 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 + 3j = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3j = 0 + -5 3j = 0 + -5 Combine like terms: 0 + -5 = -5 3j = -5 Divide each side by '3'. j = -1.666666667 Simplifying j = -1.666666667Solution
j = {3, -1.666666667}
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