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mathslover
Group Title
Show that every complex number is a root of some quadratic equation.
 2 years ago
 2 years ago
mathslover Group Title
Show that every complex number is a root of some quadratic equation.
 2 years ago
 2 years ago

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waterineyes Group TitleBest ResponseYou've already chosen the best response.0
I forgot to say : Congratulations for \(\large \color{green}{\frak{green..}}\) @mathslover
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Thanks waterineyes.
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
\((x(a+bi))(x(abi))=x^22ax+(a^2+b^2)\) So, we get that this quadratic equation has a root \(x=a+bi\). So as \(a\) and \(b\) are any real numbers we prove it for any complex number.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Hmn wait let me check it .. :)
 2 years ago

Mikael Group TitleBest ResponseYou've already chosen the best response.0
What' remarkable in @klimenkov is that his coefficients are REAL
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Oh k so there is a mistake. That is : Where is quadratic equation @klimenkov ? it must have been : \[\large{(X(a+ib))(X(a+ib))=\color{blue}{0}}\]
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Ok I meant (aib) in one of them .. :)
 2 years ago

UsukiDoll Group TitleBest ResponseYou've already chosen the best response.0
ummm what subject is this?
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
1) Equation \(x^22ax+(a^2+b^2)\) is QUADRATIC. 2) Equation \(x^22ax+(a^2+b^2)\) has a root \(x=a+bi\). 3) \(a+bi\) is any complex numer for \(a\in \mathbb R, b \in \mathbb R\).
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
Try to multiply carefully, there is no mistake.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
@klimenkov I was saying that, you didn't include 0 in RHS, why so?
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
Ah.. I'm really sorry. You are absolutely right. It was not an equation. It was just a polynomial.
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Oh no problem. That was a minor mistake ... No problem.. Thanks though.
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
@UsukiDoll this is Mathematics...
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
I like questions from people who have SmartScore > 75. Ask something interesting again!
 2 years ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
OK, if I will get a doubt, then I will like to ask you.
 2 years ago

AravindG Group TitleBest ResponseYou've already chosen the best response.1
am i late?
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
But if you have no need in real coefficients, you can just make an equation \((x(a+bi))^2=0\)
 2 years ago

AravindG Group TitleBest ResponseYou've already chosen the best response.1
@mathslover i would just observe the graph and stat this statement is true
 2 years ago

AravindG Group TitleBest ResponseYou've already chosen the best response.1
and would keep in mind that evry real number a can be written as a complex number a+0i
 2 years ago

UsukiDoll Group TitleBest ResponseYou've already chosen the best response.0
@wwaterineyes besides Mathematics. I meant what level of Mathematics is this because this certainly doesn't look like calculus or any lower level math question.
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
If you are asking for chapter then it is \(\mathsf{Complex \; \; Numbers...}\)
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Ha ha ha ha...
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
And I was just kidding...
 2 years ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
If you are asking for chapter then it is \(\text{Algebra}\).
 2 years ago

UsukiDoll Group TitleBest ResponseYou've already chosen the best response.0
oh my O_O
 2 years ago
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