If Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then
\[\prod_{n=1}^{\infty} x_n =\]
If Xn = cos \(\frac{ π}{2^n}\) + i sin\(\frac{ π}{2^n}\) , then
\[\prod_{n=1}^{\infty} x_n =\]
0
1
-1
i
The Correct Option is C
Solution and Explanation
The correct option is: (C) -1
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Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.