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Simplifying (6 + -1j)(1 + j) = 0 Multiply (6 + -1j) * (1 + j) (6(1 + j) + -1j * (1 + j)) = 0 ((1 * 6 + j * 6) + -1j * (1 + j)) = 0 ((6 + 6j) + -1j * (1 + j)) = 0 (6 + 6j + (1 * -1j + j * -1j)) = 0 (6 + 6j + (-1j + -1j2)) = 0 Combine like terms: 6j + -1j = 5j (6 + 5j + -1j2) = 0 Solving 6 + 5j + -1j2 = 0 Solving for variable 'j'. Factor a trinomial. (6 + -1j)(1 + j) = 0Subproblem 1
Set the factor '(6 + -1j)' equal to zero and attempt to solve: Simplifying 6 + -1j = 0 Solving 6 + -1j = 0 Move all terms containing j to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1j = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1j = 0 + -6 -1j = 0 + -6 Combine like terms: 0 + -6 = -6 -1j = -6 Divide each side by '-1'. j = 6 Simplifying j = 6Subproblem 2
Set the factor '(1 + j)' equal to zero and attempt to solve: Simplifying 1 + j = 0 Solving 1 + j = 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 + j = 0 + -1 Combine like terms: 1 + -1 = 0 0 + j = 0 + -1 j = 0 + -1 Combine like terms: 0 + -1 = -1 j = -1 Simplifying j = -1Solution
j = {6, -1}
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