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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 14
Total: 52
Express the following expression in the form of a + ib :
(3+i√5)(3−i√5)
(√3+√2i)−(√3−i√2)
Solution:  
We have,
(3+i√5)(3−i√5)
(√3+√2i)−(√3−i√2)
=
(3)2−(i√5)2
√3+√2i−√3+√2i
 =
9−5i2
2√2i
 =
9−5(−1)
2√2i
 =
9+5
2√2i
=
14
2√2i
 =
7
√2i
×
i
i
 =
7i
√2i2
 =
7i
√2(−1)
 =
−7i
√2(−1)
 =
−7i
√2
 =
−7×√2
√2×√2
i
(By rationalising the denominator)
=
−7√2i
2
 = 0 + i (
−7√2
2
)
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