If the set R= (a, b): a+5 b=42, a, b N has m elements and _ n=1 ^m (1-i^ n ! )=x+i y , where i= -1 , then the value of m+x+y is

Step-by-step solution

aligned & a+5 b=42, a, b N & a=42-5 b, b=1, a=37 & b=2, a=32 & b=3, a=27 & & b=8, a=2 aligned R has " 8 " elements m =8 aligned & _ n=1 ^8 (1-i^ n ! )=x+i y & for n 4, i^ n ! =1 & (1-i)+ (1-i^ 2 ! )+ (1-i^ 3 ! ) & =1-I+2+1+1 & =5-I=x+i y & m+x+y=8+5-1=12 aligned