x=-5+4i (i=-1^1/2)
Calculate the value of x^4+9x^3+35x^2-x+4...........reply soon

Question

anonymous · Answer

have answer chocies

anonymous · Answer

nopes....it is subjective

anonymous · Answer

Could you show us what you've done so far please?

anonymous · Answer

yea wat azteck said

anonymous · Answer

x+5=4i
x^2+10x+41=0
then,
x^2(x^2+10x+41)-x^3-6x^2-x+4
I dont know wt to do beyond this........

anonymous · Answer

Not quite.
What's
$$\large -1^{\frac{1}{2}}=?$$

anonymous · Answer

You wrote this i=-1^1/2 . Could you draw it using the drawing tool, because there's quite a lot of expressions that can be made when looking at that.

anonymous · Answer

$$\sqrt{-1}$$ it is related to complex no.s

anonymous · Answer

it is called iota and is represented as i

anonymous · Answer

Ah okay. Yep I see. I'm not sure, but I think it could be good to use long division.

anonymous · Answer

You know x=-5+4i is a root. So (x+5-4i) is a factor of the polynomial.

anonymous · Answer

x^2+10x+41=0 How did you get that?

anonymous · Answer

alright let me check if i am getting the answer

anonymous · Answer

ah I see, you squared both sides.

anonymous · Answer

don't think that's gonna work for you. It's best to do long diviosnl

anonymous · Answer

division*

anonymous · Answer

I may be able to use wat you've done so far. 
You have this right?
$$\large x^2+10x+41=0$$
SO we make x^2 the subject.
$$\large x^2=-10x-41$$
$$x^4+9x^3+35x^2-x+4= (-10x-41)^2+9x(-10x-41)+35(-10x-41)-x+4$$

anonymous · Answer

$$=100x^2+820x+1681-90x-369x-350x-1435-x+4$$
$$=100x^2+10x+250$$
$$=100(-10x-41)+10(-5+4i)+250$$
$$=-100x-4100-50+40i+250$$
$$=-100(-5+4i)-3900+40i$$
$$=500-400i-3900+40i$$
$$=-3400-360i$$
You can use de Moivre's theorem, but it won't give you a a precise angle. Long division wouldn't work as well as I thought it would.

anonymous · Answer

But what you did was a good start.

anonymous · Answer

that's right

anonymous · Answer

@Azteck  i will tell you something tht long division works better. first squaring as in x^2 + 10x + 41 Then dividing x^4+9x^3+35x^2-x+4 and u get the quotient as x^2-x+4 and remainder -160. we know that x^2+10x+41 = 0. So when we multiply Quotient with divisor we get 0. and the remainder -160 is the answer.

anonymous · Answer

@Azteck  Thanks for ur help anyways

anonymous · Answer

ur welcome

anonymous · Answer

@snowman97 I said thanks to @Azteck

anonymous · Answer

want to message each other

anonymous · Answer

@snowman97 Abt wt? and why?

anonymous · Answer

just talk

anonymous · Answer

Now worries.

anonymous · Answer

no*

anonymous · Answer

hmmm