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Simplifying (4 + -1j)(-1 + 4j) = 0 Multiply (4 + -1j) * (-1 + 4j) (4(-1 + 4j) + -1j * (-1 + 4j)) = 0 ((-1 * 4 + 4j * 4) + -1j * (-1 + 4j)) = 0 ((-4 + 16j) + -1j * (-1 + 4j)) = 0 (-4 + 16j + (-1 * -1j + 4j * -1j)) = 0 (-4 + 16j + (1j + -4j2)) = 0 Combine like terms: 16j + 1j = 17j (-4 + 17j + -4j2) = 0 Solving -4 + 17j + -4j2 = 0 Solving for variable 'j'. Factor a trinomial. (-4 + j)(1 + -4j) = 0Subproblem 1
Set the factor '(-4 + j)' equal to zero and attempt to solve: Simplifying -4 + j = 0 Solving -4 + j = 0 Move all terms containing j to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + j = 0 + 4 Combine like terms: -4 + 4 = 0 0 + j = 0 + 4 j = 0 + 4 Combine like terms: 0 + 4 = 4 j = 4 Simplifying j = 4Subproblem 2
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 = 0.25Solution
j = {4, 0.25}
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