If (a + bi)(a - bi) = 61 and a + b = 11 then a² + b² equals?
- 61
- 62
- 63
- 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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