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Question

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

A
x2y2
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B
x2+y2
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C
x4y4
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D
x4+y4
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Solution

The correct option is C x2+y2
Given,
(2+i)(2+2i)(2+3i).......(2+ni)=x+iy.
Now taking modulus both sides we get,
|(2+i)(2+2i)(2+3i).......(2+ni)|=|x+iy|
or, |(2+i)|.|(2+2i)|.|(2+3i)|........|(2+ni)|=|x+iy| [ Since |a.b|=|a|.|b| for a,b being complex number]
or, 5.8.13......(4+n2)=x2+y2

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