Fool's problem of the day,

Find the value of $ x^4 +9x^3+35x^2-x+4$ for $ x = -5+2\sqrt{-4}$

Question

Fool's problem of the day,

Find the value of  $ x^4 +9x^3+35x^2-x+4$ for $ x = -5+2\sqrt{-4}$

anonymous · Answer

Ishaan I am expecting an answer of you :)

anonymous · Answer

umm yeah, I am trying to find an easier, smart and quick way to do it.

anonymous · Answer

well of-course, the standard substation is not feasible without electronic aid.

anonymous · Answer

this is embarassing it seems so easy

anonymous · Answer

I agree ishaan :D

anonymous · Answer

Here comes mighty asnaseer!

asnaseer · Answer

isn't this just a simple substitution of $x=-5+4i$ into the above equation?

anonymous · Answer

Yes asnaseer but that would be messy/tedious isn't ?

asnaseer · Answer

the equation could be rearranged to:$$x(x(x(x+9)+35)-1)+4$$to simplify the calculations

asnaseer · Answer

or maybe find some rearrangement to get terms involving:$$x(x-8i)=(-5+4i)(-5-4i)=25+16=41$$

anonymous · Answer

You did it again asnaseer! :)

asnaseer · Answer

I did? I know the answer but I am trying to see how I can make use of my last idea?

anonymous · Answer

160 but this was so embarassing for me :-/

asnaseer · Answer

-160

anonymous · Answer

I like this one $ x(x(x(x+9)+35)-1)+4 $

asnaseer · Answer

thats the one I used.

asnaseer · Answer

I thought maybe $x(x-8i)$ might be useable somehow but can't see how.

anonymous · Answer

I can't either.

asnaseer · Answer

:) phew! - so you ARE mortal :D

anonymous · Answer

lol, you may never know :P

anonymous · Answer