If (a + bi)(a - bi) = 89 and a+ b = 10 then a² + b² equals?
- 89
- 90
- 91
- None of these
Explanation
If you multiply (a + bi) and (a - bi), you get:
(a + bi)(a - bi) = a_a - a_bi + bi_a - bi_bi
= a^2 - abi + abi - b^2_i^2
The middle terms cancel out. And i^2 = -1, so -b^2_i^2 = -b^2*(-1) = b^2.
That leaves a^2 + b^2.
You are told (a + bi)(a - bi) = 89, so a^2 + b^2 = 89.
Last verified on 25-05-2026
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