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Simplifying (2 + -5i) + -1(3 + 4i) + -1(-2 + i) = 0 Remove parenthesis around (2 + -5i) 2 + -5i + -1(3 + 4i) + -1(-2 + i) = 0 2 + -5i + (3 * -1 + 4i * -1) + -1(-2 + i) = 0 2 + -5i + (-3 + -4i) + -1(-2 + i) = 0 2 + -5i + -3 + -4i + (-2 * -1 + i * -1) = 0 2 + -5i + -3 + -4i + (2 + -1i) = 0 Reorder the terms: 2 + -3 + 2 + -5i + -4i + -1i = 0 Combine like terms: 2 + -3 = -1 -1 + 2 + -5i + -4i + -1i = 0 Combine like terms: -1 + 2 = 1 1 + -5i + -4i + -1i = 0 Combine like terms: -5i + -4i = -9i 1 + -9i + -1i = 0 Combine like terms: -9i + -1i = -10i 1 + -10i = 0 Solving 1 + -10i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -10i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10i = 0 + -1 -10i = 0 + -1 Combine like terms: 0 + -1 = -1 -10i = -1 Divide each side by '-10'. i = 0.1 Simplifying i = 0.1
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