If [(1-i)/(1+i)]100 =a+ib, then find (a,b) - Maths - Complex Numbers and Quadratic Equations

Question

If [(1-i)/(1+i)]100 =a+ib, then find (a,b)

A K Daya Sir · Accepted Answer

[(1-i)/(1+i)]100 =a+ib
Lets rationalise it
[(1 - i)(1 - i) / (1 + i)(1 - i)]100 =a+ib
[ (1 - i)2 / (1 - i2 ) ]100 = a
+ ib
[(1 + i2 - 2i) / 2 ]100 = a + ib
[-2i/2]100 = a + ib
(-i)100 = a + ib
[(-i)2 ]50 = a + ib
(-1)50 = a + ib
1 = a + ib
a = 1
b = 0