Question

If \(T_0,T_1,T_2,\ldots,T_n\) represent the terms in the expansion of \((x+a)^n\), then \((T_0-T_2+T_4-\cdots)^2+(T_1-T_3+T_5-\cdots)^2=\)

• A. \((x^2+a^2)^n\)
• B. \((x^2+a^2)^{2n}\)
• C. \((x^2+a^2)^{n/2}\)
• D. \((x^2+a^2)^{-1/n}\)

Hint:

Complex numbers simplify alternating binomial sums.

Answer 1

The Correct Option is A

Step 1: Consider \((x+ai)^n\).
Step 2: Separate real and imaginary parts.
Step 3: Square and add to obtain: \[ (x^2+a^2)^n \]