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Simplifying [1000 + 0.5(4000) + -200i] = 0 Multiply 0.5 * 4000 [1000 + 2000 + -200i] = 0 Combine like terms: 1000 + 2000 = 3000 [3000 + -200i] = 0 Remove brackets around [3000 + -200i] 3000 + -200i = 0 Solving 3000 + -200i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3000' to each side of the equation. 3000 + -3000 + -200i = 0 + -3000 Combine like terms: 3000 + -3000 = 0 0 + -200i = 0 + -3000 -200i = 0 + -3000 Combine like terms: 0 + -3000 = -3000 -200i = -3000 Divide each side by '-200'. i = 15 Simplifying i = 15
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