F.4 Maths

[(1+i)⁹]/[(1-i)⁸]=[(1+i)/(1-i)]⁸(1+i)={[(1+i)(1+i)]/[(1-i)(1+i)]}⁸(1+i)=[(1+2i+i²)/(1-i²)]⁸(1+i)=[(1+2i-1)/(1+1)]⁸(1+i)=[(2i)/2]⁸(1+i)=i⁸(1+i)=1(1+i) =1+i

(1+i)^(9)/(1-i)^(8)
={(1+i)/(1-i)]^8(1+i)
={[(1+i)/(1-i)]*[(1+i)/(1+i)]}^8(1+i)
=[(1+2i-1)/2]^8(1+i)
=(2i/2)^8(1+i)
=i^8(1+i)
=1(1+i)
=1+i

(1+ i)^9/(1 - i)^8

= (1+ i)^9(1 + i)^8/(1 - i)^8(1 + i)^8

= (1+ i)^17/256

= (√2)^17[cos(17π/4) + isin(17π/4)]/256

= √2[cos(π/4) + isin(π/4)]

= 1 + i