Question

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

Answer 1

hope this helps you☺️

Answer 2

Answer:

a=1 and b=0

Step-by-step explanation:

The given equation is:

$(\frac{1-i}{1+i})^{100}=a+ib$

Upon solving the above equation, we get

$(\frac{1-i}{1+i}{\times}\frac{1-i}{1-i})^{100}=a+ib$

$(\frac{1+i^2-2i}{2})^{100}=a+ib$

$(\frac{1-1-2i}{2})^{100}=a+ib$

$(-i)^{100}=a+ib$

$(-i^2)^{50}=a+ib$

$1=a+ib$

Thus, on comparing, a=1 and b=0.