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

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

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To solve the problem \(\left(\frac{1-i}{1+i}\right)^{100} = a + ib\), we will follow these steps: ### Step 1: Simplify \(\frac{1-i}{1+i}\) To simplify the expression \(\frac{1-i}{1+i}\), we multiply the numerator and the denominator by the conjugate of the denominator: \[ \frac{1-i}{1+i} \cdot \frac{1-i}{1-i} = \frac{(1-i)(1-i)}{(1+i)(1-i)} ...
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