- Home
- Standard 11
- Mathematics
4-1.Complex numbers
medium
જો $(1 + i)(1 + 2i)(1 + 3i).....(1 + ni) = a + ib$ તો $2.5.10....$$(1 + {n^2})$ = . . . .
A
${a^2} - {b^2}$
B
${a^2} + {b^2}$
C
$\sqrt {{a^2} + {b^2}} $
D
$\sqrt {{a^2} - {b^2}} $
Solution
(b)We have
$(1 + i)(1 + 2i)(1 + 3i)…..(1 + ni) = a + ib$ …..$(i)$
==> $(1 – i)(1 – 2i)(1 – 3i)…..(1 – ni) = a – ib$ …..$(ii)$
Multiplying $ (i)$ and $(ii)$, we get $2.5…..(1 + {n^2}) = {a^2} + {b^2}$
Standard 11
Mathematics
