Question

A function 'f' is defined by f(z) = (4 + i)z2 + az + y for all complex number z, where a and y are complex
numbers if f(1) and f(i) are both real then the smallest possible values of ſal +ly is (take V2 = 1.417)​

Answer 1

Answer:

Its clear that it is a linear function with 0 constant, as

\begin{gathered}f(x) = mx +n\\f(x)+f(y) =f(x+y)\\m(x+y) +2n = m(x+y) +n\\2n=n\\n=0\end{gathered}

f(x)=mx+n

f(x)+f(y)=f(x+y)

m(x+y)+2n=m(x+y)+n

2n=n

n=0