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