NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions
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Question : 51
Total: 52
If (a + ib)(c + id)(e + if)(g + ih) = A + iB, then show that ( a 2 + b 2 ) ( c 2 + d 2 ) ( e 2 + f 2 ) ( g 2 + h 2 ) ( A 2 + B 2 )
Solution:
We have, (a + ib)(c + id)(e + if)(g + ih) = A + iB
∴ |(a + ib)(c + id)(e + if)(g + ih)| = |A + iB|
⇒ |a + ib||c + id||e + if||g + ih| = |A + iB|
⇒√ a 2 + b 2 √ c 2 + d 2 √ e 2 + f 2 √ g 2 + h 2 √ A 2 + B 2
Squaring (i) both sides, we get,( a 2 + b 2 ) ( c 2 + d 2 ) ( e 2 + f 2 ) ( g 2 + h 2 ) A 2 + B 2
∴ |(a + ib)(c + id)(e + if)(g + ih)| = |A + iB|
⇒ |a + ib||c + id||e + if||g + ih| = |A + iB|
⇒
Squaring (i) both sides, we get,
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