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Simplifying (a + bi)(8 + 6i) = 1 Multiply (a + bi) * (8 + 6i) (a(8 + 6i) + bi(8 + 6i)) = 1 ((8 * a + 6i * a) + bi(8 + 6i)) = 1 ((8a + 6ai) + bi(8 + 6i)) = 1 (8a + 6ai + (8 * bi + 6i * bi)) = 1 (8a + 6ai + (8bi + 6bi2)) = 1 (8a + 6ai + 8bi + 6bi2) = 1 Solving 8a + 6ai + 8bi + 6bi2 = 1 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8bi' to each side of the equation. 8a + 6ai + 8bi + -8bi + 6bi2 = 1 + -8bi Combine like terms: 8bi + -8bi = 0 8a + 6ai + 0 + 6bi2 = 1 + -8bi 8a + 6ai + 6bi2 = 1 + -8bi Add '-6bi2' to each side of the equation. 8a + 6ai + 6bi2 + -6bi2 = 1 + -8bi + -6bi2 Combine like terms: 6bi2 + -6bi2 = 0 8a + 6ai + 0 = 1 + -8bi + -6bi2 8a + 6ai = 1 + -8bi + -6bi2 Reorder the terms: -1 + 8a + 6ai + 8bi + 6bi2 = 1 + -8bi + -6bi2 + -1 + 8bi + 6bi2 Reorder the terms: -1 + 8a + 6ai + 8bi + 6bi2 = 1 + -1 + -8bi + 8bi + -6bi2 + 6bi2 Combine like terms: 1 + -1 = 0 -1 + 8a + 6ai + 8bi + 6bi2 = 0 + -8bi + 8bi + -6bi2 + 6bi2 -1 + 8a + 6ai + 8bi + 6bi2 = -8bi + 8bi + -6bi2 + 6bi2 Combine like terms: -8bi + 8bi = 0 -1 + 8a + 6ai + 8bi + 6bi2 = 0 + -6bi2 + 6bi2 -1 + 8a + 6ai + 8bi + 6bi2 = -6bi2 + 6bi2 Combine like terms: -6bi2 + 6bi2 = 0 -1 + 8a + 6ai + 8bi + 6bi2 = 0 The solution to this equation could not be determined.
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