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Simplifying (-4 + -1i) + -1(2 + 3i) + (-4 + 5i) = 0 Remove parenthesis around (-4 + -1i) -4 + -1i + -1(2 + 3i) + (-4 + 5i) = 0 -4 + -1i + (2 * -1 + 3i * -1) + (-4 + 5i) = 0 -4 + -1i + (-2 + -3i) + (-4 + 5i) = 0 Remove parenthesis around (-4 + 5i) -4 + -1i + -2 + -3i + -4 + 5i = 0 Reorder the terms: -4 + -2 + -4 + -1i + -3i + 5i = 0 Combine like terms: -4 + -2 = -6 -6 + -4 + -1i + -3i + 5i = 0 Combine like terms: -6 + -4 = -10 -10 + -1i + -3i + 5i = 0 Combine like terms: -1i + -3i = -4i -10 + -4i + 5i = 0 Combine like terms: -4i + 5i = 1i -10 + 1i = 0 Solving -10 + 1i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 1i = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 1i = 0 + 10 1i = 0 + 10 Combine like terms: 0 + 10 = 10 1i = 10 Divide each side by '1'. i = 10 Simplifying i = 10
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