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Simplifying 6.5(j + -5) = 2(0.75 + -1j) Reorder the terms: 6.5(-5 + j) = 2(0.75 + -1j) (-5 * 6.5 + j * 6.5) = 2(0.75 + -1j) (-32.5 + 6.5j) = 2(0.75 + -1j) -32.5 + 6.5j = (0.75 * 2 + -1j * 2) -32.5 + 6.5j = (1.5 + -2j) Solving -32.5 + 6.5j = 1.5 + -2j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '2j' to each side of the equation. -32.5 + 6.5j + 2j = 1.5 + -2j + 2j Combine like terms: 6.5j + 2j = 8.5j -32.5 + 8.5j = 1.5 + -2j + 2j Combine like terms: -2j + 2j = 0 -32.5 + 8.5j = 1.5 + 0 -32.5 + 8.5j = 1.5 Add '32.5' to each side of the equation. -32.5 + 32.5 + 8.5j = 1.5 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 8.5j = 1.5 + 32.5 8.5j = 1.5 + 32.5 Combine like terms: 1.5 + 32.5 = 34 8.5j = 34 Divide each side by '8.5'. j = 4 Simplifying j = 4
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