Let
f(z) = 2z if z is not real
f(z) = -2z if z is real
Find f(f(f(f(1 + i)))).
Multiplying by a constant will not conver the imaginary number to a real number so
f(1+i) = 2 + 2i
f(2+ 2i) = 4 + 4i
f(4+4i) = 8 + 8i
f(8+8i) = 16 + 16i