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Simplifying (14 + -8j)(2 + 3j) = 0 Multiply (14 + -8j) * (2 + 3j) (14(2 + 3j) + -8j * (2 + 3j)) = 0 ((2 * 14 + 3j * 14) + -8j * (2 + 3j)) = 0 ((28 + 42j) + -8j * (2 + 3j)) = 0 (28 + 42j + (2 * -8j + 3j * -8j)) = 0 (28 + 42j + (-16j + -24j2)) = 0 Combine like terms: 42j + -16j = 26j (28 + 26j + -24j2) = 0 Solving 28 + 26j + -24j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 13j + -12j2) = 0 Factor a trinomial. 2((7 + -4j)(2 + 3j)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -4j)' equal to zero and attempt to solve: Simplifying 7 + -4j = 0 Solving 7 + -4j = 0 Move all terms containing j to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4j = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4j = 0 + -7 -4j = 0 + -7 Combine like terms: 0 + -7 = -7 -4j = -7 Divide each side by '-4'. j = 1.75 Simplifying j = 1.75Subproblem 2
Set the factor '(2 + 3j)' equal to zero and attempt to solve: Simplifying 2 + 3j = 0 Solving 2 + 3j = 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 + 3j = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3j = 0 + -2 3j = 0 + -2 Combine like terms: 0 + -2 = -2 3j = -2 Divide each side by '3'. j = -0.6666666667 Simplifying j = -0.6666666667Solution
j = {1.75, -0.6666666667}
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