Question

Please help me solve the following sum on complex numbers:

Answer 1

GIven that (3+2i) is a root of \[2x^3 + px^2 + 20x + q = 0\] and p and q are real numbers, find p and q (finding the other roots is the next part of the question which I could do much more easily, no worries :P)

Answer 2

put x = 3 + 2i, and simplify simplify ... and compare the real and imaginary part of both sides.

Answer 3

oh whoops, thank you so much :D

Answer 4

and for other roots, factor out (x - 3 - 2i) <-- this can be quite troublesome.

Answer 5

see, one of the roots has to be 3-2i, right?

Answer 6

oh ,, yes yes ... right, it's cubic equation.

Answer 7

then we multiply those two, and divide?? idk, lemme work it out and see.

Answer 8

best way is to guess the root by remainder theorem. else you can factor out
(x^2 - 6x + 13)

Answer 9

what do you mean by compare the imaginary and real things on both sides??

Answer 10

Just set x = 3+2i for now... and simplify.

Answer 11

I did that. The previous part of the question said find x^2 and x^3 if x = 3+2i. I'm wondering, maybe i've got that wrong

Answer 12

\[\Large 2(3+2i)^3+\color{red}p(3+2i)^2+20(3+2i)+\color{blue}q=0\]

Answer 13

OH MY GOD. I JUST REALIZED

Answer 14

What IS the cube and square of 3+2i?

Answer 15

so instead of multiplying normally, I went and used de moivres theorem, and got some really weird answers

Answer 16

de moivre?
You actually used polar forms? -.-

Answer 17

waste of time, and energy, and brain power. UGH

Answer 18

So... I take it you get it now? ^_^

Answer 19

Hey... everything okay?