anonymous
  • anonymous
Please help me solve the following sum on complex numbers:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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)
experimentX
  • experimentX
put x = 3 + 2i, and simplify simplify ... and compare the real and imaginary part of both sides.
anonymous
  • anonymous
oh whoops, thank you so much :D

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experimentX
  • experimentX
and for other roots, factor out (x - 3 - 2i) <-- this can be quite troublesome.
anonymous
  • anonymous
see, one of the roots has to be 3-2i, right?
experimentX
  • experimentX
oh ,, yes yes ... right, it's cubic equation.
anonymous
  • anonymous
then we multiply those two, and divide?? idk, lemme work it out and see.
experimentX
  • experimentX
best way is to guess the root by remainder theorem. else you can factor out (x^2 - 6x + 13)
anonymous
  • anonymous
what do you mean by compare the imaginary and real things on both sides??
terenzreignz
  • terenzreignz
Just set x = 3+2i for now... and simplify.
anonymous
  • anonymous
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
terenzreignz
  • terenzreignz
\[\Large 2(3+2i)^3+\color{red}p(3+2i)^2+20(3+2i)+\color{blue}q=0\]
anonymous
  • anonymous
OH MY GOD. I JUST REALIZED
terenzreignz
  • terenzreignz
What IS the cube and square of 3+2i?
anonymous
  • anonymous
so instead of multiplying normally, I went and used de moivres theorem, and got some really weird answers
terenzreignz
  • terenzreignz
de moivre? You actually used polar forms? -.-
anonymous
  • anonymous
waste of time, and energy, and brain power. UGH
terenzreignz
  • terenzreignz
So... I take it you get it now? ^_^
terenzreignz
  • terenzreignz
Hey... everything okay?

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