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Simplifying 60 = 124j + -8j2 Solving 60 = 124j + -8j2 Solving for variable 'j'. Reorder the terms: 60 + -124j + 8j2 = 124j + -124j + -8j2 + 8j2 Combine like terms: 124j + -124j = 0 60 + -124j + 8j2 = 0 + -8j2 + 8j2 60 + -124j + 8j2 = -8j2 + 8j2 Combine like terms: -8j2 + 8j2 = 0 60 + -124j + 8j2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -31j + 2j2) = 0 Factor a trinomial. 4((1 + -2j)(15 + -1j)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2j)' equal to zero and attempt to solve: Simplifying 1 + -2j = 0 Solving 1 + -2j = 0 Move all terms containing j to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2j = 0 + -1 -2j = 0 + -1 Combine like terms: 0 + -1 = -1 -2j = -1 Divide each side by '-2'. j = 0.5 Simplifying j = 0.5Subproblem 2
Set the factor '(15 + -1j)' equal to zero and attempt to solve: Simplifying 15 + -1j = 0 Solving 15 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1j = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1j = 0 + -15 -1j = 0 + -15 Combine like terms: 0 + -15 = -15 -1j = -15 Divide each side by '-1'. j = 15 Simplifying j = 15Solution
j = {0.5, 15}
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