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If (a + bi)(a - bi) = 61 and a + b = 11 then a² + b² equals?
  1. 61
  2. 62
  3. 63
  4. None of these
Explanation

(a + bi)(a - bi) is the product of conjugates.  

(a + bi)(a - bi) = a² - (bi)² = a² - b²i²  

Since i² = -1:  

= a² - b²(-1) = a² + b²  

Given (a + bi)(a - bi) = 61,  

so a² + b² = 61.


Last verified on 24-05-2026

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