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  • If  then the expansion of <img alt="(x+i y)^{n}+(x-i y)^{n}" src="http://entrancecor

If i=\sqrt{-1} then the expansion of (x+i y)^{n}+(x-i y)^{n} is

Option: 1

Purely Real


Option: 2

Real and Imaginary


Option: 3

Purely Imaginary


Option: 4

None of the above


Answers (1)

best_answer

As  \mathrm{(x+y)^{n}+(x-y)^{n}=2\left[^{n} C_{0}\; x^{n}\; y^{0}+^{n} C_{2} \;x^{n-2}\; y^{2}+^{n} C_{4}\; x^{n-4} \;y^{4}+\ldots .\right]}

Hence,

(x+iy)^{n}+(x-iy)^{n}=2\left[^{n} C_{0} x^{n} (iy)^{0}+^{n} C_{2}\; x^{n-2} (iy)^{2}\cdots\cdots]\right.

it is clear that the index of i is even and even power of i becomes real

hence the expansion becomes purely real

 

option A is correct

Posted by

Ritika Harsh

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