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