Question
Question: If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = a + ib, then 2 .5 . 10 …… (1 + n<sup>2</sup>) =...
If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = a + ib, then 2 .5 . 10 …… (1 + n2) =
A
a - ib
B
a2 – b2
C
a2 + b2
D
None of these
Answer
a2 + b2
Explanation
Solution
Sol. Taking modulus and squaring on both sides
(1 + i)2 . (1 + 2i)2 ………. |1 + ni|2 = |a + ib|2
(1 + 1) . (1 + 4) .……... (1 + n2) = a2 + b2 2 . 5 . 10 . …………. (1 + n2) = a2 + b2