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If (a + bi)(a - bi) = 53 and a + b = 8 then a² + b² equals?
  1. 52
  2. 53
  3. 54
  4. None of these
Explanation

(a + bi)(a - bi) = a^2 - (bi)^2 = a^2 - b^2 _ i^2

Since i^2 = -1, this becomes:

a^2 - b^2 _ (-1) = a^2 + b^2

Given (a + bi)(a - bi) = 53,

a^2 + b^2 = 53


Last verified on 23-05-2025

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