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Simplifying (-4 + -5j)(3 + -2j) = 0 Multiply (-4 + -5j) * (3 + -2j) (-4(3 + -2j) + -5j * (3 + -2j)) = 0 ((3 * -4 + -2j * -4) + -5j * (3 + -2j)) = 0 ((-12 + 8j) + -5j * (3 + -2j)) = 0 (-12 + 8j + (3 * -5j + -2j * -5j)) = 0 (-12 + 8j + (-15j + 10j2)) = 0 Combine like terms: 8j + -15j = -7j (-12 + -7j + 10j2) = 0 Solving -12 + -7j + 10j2 = 0 Solving for variable 'j'. Factor a trinomial. (-4 + -5j)(3 + -2j) = 0Subproblem 1
Set the factor '(-4 + -5j)' equal to zero and attempt to solve: Simplifying -4 + -5j = 0 Solving -4 + -5j = 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 + -5j = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5j = 0 + 4 -5j = 0 + 4 Combine like terms: 0 + 4 = 4 -5j = 4 Divide each side by '-5'. j = -0.8 Simplifying j = -0.8Subproblem 2
Set the factor '(3 + -2j)' equal to zero and attempt to solve: Simplifying 3 + -2j = 0 Solving 3 + -2j = 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 + -2j = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2j = 0 + -3 -2j = 0 + -3 Combine like terms: 0 + -3 = -3 -2j = -3 Divide each side by '-2'. j = 1.5 Simplifying j = 1.5Solution
j = {-0.8, 1.5}
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