If (a + bi)(a - bi) = 53 and a + b = 8 then a² + b² equals?
- 52
- 53
- 54
- 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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