Question

If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n²) = ______.

Answer 1

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.