Polynomial/f(i) is 1,f(1) is 1+i,f(1-2i) is -i/System of equations/Exercise

Find a polynomial

${}f=a+bX+cX^{2}\,$

with ${}a,b,c\in \mathbb {C}$, such that the following conditions hold.

$f({\mathrm {i} })=1,\,f(1)=1+{\mathrm {i} },\,f(1-2{\mathrm {i} })=-{\mathrm {i} }.$

Create a solution