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Simplifying (4j + 1)(4j + -4) = 0 Reorder the terms: (1 + 4j)(4j + -4) = 0 Reorder the terms: (1 + 4j)(-4 + 4j) = 0 Multiply (1 + 4j) * (-4 + 4j) (1(-4 + 4j) + 4j * (-4 + 4j)) = 0 ((-4 * 1 + 4j * 1) + 4j * (-4 + 4j)) = 0 ((-4 + 4j) + 4j * (-4 + 4j)) = 0 (-4 + 4j + (-4 * 4j + 4j * 4j)) = 0 (-4 + 4j + (-16j + 16j2)) = 0 Combine like terms: 4j + -16j = -12j (-4 + -12j + 16j2) = 0 Solving -4 + -12j + 16j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -3j + 4j2) = 0 Factor a trinomial. 4((-1 + -4j)(1 + -1j)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -4j)' equal to zero and attempt to solve: Simplifying -1 + -4j = 0 Solving -1 + -4j = 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 + -4j = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4j = 0 + 1 -4j = 0 + 1 Combine like terms: 0 + 1 = 1 -4j = 1 Divide each side by '-4'. j = -0.25 Simplifying j = -0.25Subproblem 2
Set the factor '(1 + -1j)' equal to zero and attempt to solve: Simplifying 1 + -1j = 0 Solving 1 + -1j = 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 + -1j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1j = 0 + -1 -1j = 0 + -1 Combine like terms: 0 + -1 = -1 -1j = -1 Divide each side by '-1'. j = 1 Simplifying j = 1Solution
j = {-0.25, 1}
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