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Simplifying -3(-11 + -5i) + 5(2 + -11i) = 0 (-11 * -3 + -5i * -3) + 5(2 + -11i) = 0 (33 + 15i) + 5(2 + -11i) = 0 33 + 15i + (2 * 5 + -11i * 5) = 0 33 + 15i + (10 + -55i) = 0 Reorder the terms: 33 + 10 + 15i + -55i = 0 Combine like terms: 33 + 10 = 43 43 + 15i + -55i = 0 Combine like terms: 15i + -55i = -40i 43 + -40i = 0 Solving 43 + -40i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + -40i = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -40i = 0 + -43 -40i = 0 + -43 Combine like terms: 0 + -43 = -43 -40i = -43 Divide each side by '-40'. i = 1.075 Simplifying i = 1.075
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