If `((1-i)/(1+i))^(100)=a+i b` , find`(a , b)`

Explanation

To solve the problem \(\left(\frac{1-i}{1+i}\right)^{100} = a + ib\), we will follow these steps:

### Step 1: Simplify the expression \(\frac{1-i}{1+i}\)

To simplify \(\frac{1-i}{1+i}\), we multiply the numerator and denominator by the conjugate of the denominator, which is \(1-i\):

\[
\frac{1-i}{1+i} \cdot \frac{1-i}{1-i} = \frac{(1-i)(1-i)}{(1+i)(1-i)}
...