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Simplifying 1 + -1i + i2 = 0.75 Solving 1 + -1i + i2 = 0.75 Solving for variable 'i'. Reorder the terms: 1 + -0.75 + -1i + i2 = 0.75 + -0.75 Combine like terms: 1 + -0.75 = 0.25 0.25 + -1i + i2 = 0.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.25 + -1i + i2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1i + -0.25 + i2 = 0.00 + -0.25 Reorder the terms: 0.25 + -0.25 + -1i + i2 = 0.00 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1i + i2 = 0.00 + -0.25 -1i + i2 = 0.00 + -0.25 Combine like terms: 0.00 + -0.25 = -0.25 -1i + i2 = -0.25 The i term is -1i. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1i + 0.25 + i2 = -0.25 + 0.25 Reorder the terms: 0.25 + -1i + i2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -1i + i2 = 0.00 Factor a perfect square on the left side: (i + -0.5)(i + -0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (i + -0.5) equal to 0.00 and 0.00.Subproblem 1
i + -0.5 = 0.00 Simplifying i + -0.5 = 0.00 Reorder the terms: -0.5 + i = 0.00 Solving -0.5 + i = 0.00 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + i = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + i = 0.00 + 0.5 i = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 i = 0.5 Simplifying i = 0.5Subproblem 2
i + -0.5 = 0.00 Simplifying i + -0.5 = 0.00 Reorder the terms: -0.5 + i = 0.00 Solving -0.5 + i = 0.00 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + i = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + i = 0.00 + 0.5 i = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 i = 0.5 Simplifying i = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. i = {0.5, 0.5}
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