Find the modulus of [(1+i)/(1-i)] – [(1-i)/(1+i)]

dsgbfbhdfrhredsbgrdghr

Welcome to AskIITians

Given: [(1+i)/(1-i)] – [(1-i)/(1+i)]

Simplify the given expression, we get:[(1+i)/(1-i)] – [(1-i)/(1+i)] = [(1+i)^2– (1-i)^2]/ [(1+i)(1-i)]= (1+i^2+2i-1-i^2+2i)) / (1^2+1^2)

Now, cancel out the terms,

= 4i / 2

= 2i

Now, take the modulus,

| [(1+i)/(1-i)] – [(1-i)/(1+i)]| =|2i| = √2^2= 2

Therefore, the modulus of [(1+i)/(1-i)] – [(1-i)/(1+i)] is 2.

Thanks