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Question
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
Solution
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
Explanation:
Given that (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy .....(1)
⇒ `(bar(2 + i)) (bar(2 + 2i)) (bar(2 + 3i)) ... (bar(2 + ni)) = (bar(x + iy))` = (x – iy)
i.e., (2 – i) (2 – 2i) (2 – 3i) ... (2 – ni) = x – iy ......(2)
Multiplying (1) and (2)
We get 5.8.13 ... (4 + n2) = x2 + y2.
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