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Simplifying (4 + -7j)(3 + -4j) = 0 Multiply (4 + -7j) * (3 + -4j) (4(3 + -4j) + -7j * (3 + -4j)) = 0 ((3 * 4 + -4j * 4) + -7j * (3 + -4j)) = 0 ((12 + -16j) + -7j * (3 + -4j)) = 0 (12 + -16j + (3 * -7j + -4j * -7j)) = 0 (12 + -16j + (-21j + 28j2)) = 0 Combine like terms: -16j + -21j = -37j (12 + -37j + 28j2) = 0 Solving 12 + -37j + 28j2 = 0 Solving for variable 'j'. Factor a trinomial. (4 + -7j)(3 + -4j) = 0Subproblem 1
Set the factor '(4 + -7j)' equal to zero and attempt to solve: Simplifying 4 + -7j = 0 Solving 4 + -7j = 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 + -7j = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7j = 0 + -4 -7j = 0 + -4 Combine like terms: 0 + -4 = -4 -7j = -4 Divide each side by '-7'. j = 0.5714285714 Simplifying j = 0.5714285714Subproblem 2
Set the factor '(3 + -4j)' equal to zero and attempt to solve: Simplifying 3 + -4j = 0 Solving 3 + -4j = 0 Move all terms containing j to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4j = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4j = 0 + -3 -4j = 0 + -3 Combine like terms: 0 + -3 = -3 -4j = -3 Divide each side by '-4'. j = 0.75 Simplifying j = 0.75Solution
j = {0.5714285714, 0.75}
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