JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \( z=(1+i)(1+2i)(1+3i)\dots(1+ni), \) where \( i=\sqrt{-1}. \) If \( |z|^{2}=44200, \) then \( n \) is equal to
- A 4
- B 5
- C 6
- D 7
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\(|z|^2=2^3 \cdot 5^2 \cdot 13 \cdot 17\) \(\prod_{r=1}^n\left(1+r^2\right)=2^3 \cdot 5^2 \cdot 13 \cdot 17=(2) \cdot(5) \cdot(2 \cdot 5) \cdot(17) \cdot(2 \cdot 13)=2 \cdot 5 \cdot 10 \cdot 17 \cdot 26\) \(\text { so } n=5\)
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