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

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Question : 43
Total: 52
If a + ib =
(x+i)2
2x2+1
 , prove that a2+b2 =
(x2+1)2
(2x2+1)2
Solution:  
We have, a + ib =
(x+i)2
2x2+1
∴ |a + ib| = |
(x+i)2
2x2+1
| =
|(x+i)2|
|2x2+1|
 =
|x+i|2
|2x2+1|
⇒ √a2+b2 =
√(x2+12)2
√(2x2+1)2
 ... (i)
Squaring (i) both sides, we get
a2+b2 =
(x2+1)2
(2x2+1)2
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