Question

If (1 + i) (1 + 2i) (1 + 3i)…(1 + ni) = x + iy, then 2.5.10……(1 + n²) is _____ 

(a) 1 

(b) i

(c) x² + y² 

(d) 1 + n²

Answer 1

(c) The answer is x² + y²

Answer 2

If (1 + i) (1 + 2i) (1 + 3i)…(1 + ni) = x + iy, then 2.5.10……(1 + n2) is _____

|(1 + i) (1 + 2i) (1 + 3i)…(1 + ni)| = |x + iy|

|(1 + i) (1 + 2i) (1 + 3i)…(1 + ni)|² = |x + iy|²      { using |z₁z₂| = |z₁||z₂|  }

|(1 + i)|² |(1 + 2i)|² |(1 + 3i)|² .....|(1 + ni)|² = x²+y²

2 . 5. 10 .... ( 1+n²)  = x²+y²