Division involving a complex number
up vote
0
down vote
favorite
Given this
$dfrac{x+1}{x-i}$
What can I do with that?
If i do polynomial division as below, I get:
$$x-i)overline{x+1} = 1 + frac{1+i}{x-1}$$
however, I'm not even sure if this is legal maths.
The other thing I think I could to is remove the complex demoninator with the complex conjugate to get:
$$dfrac{x^2-x(i-1)-i}{x^2+1}$$
but I do not know what to do with this from this point on. I tried polynomial division to get:
$$1- frac{-x(i-1)-1}{x^2+1}$$
Once again, i'm not sure if this is the correct path.
Some help would be appreciated.
Thanks
polynomials complex-numbers
asked Nov 23 at 13:34
Bucephalus
660417
add a comment |
up vote
0
down vote
favorite
Given this
$dfrac{x+1}{x-i}$
What can I do with that?
If i do polynomial division as below, I get:
$$x-i)overline{x+1} = 1 + frac{1+i}{x-1}$$
however, I'm not even sure if this is legal maths.
The other thing I think I could to is remove the complex demoninator with the complex conjugate to get:
$$dfrac{x^2-x(i-1)-i}{x^2+1}$$
but I do not know what to do with this from this point on. I tried polynomial division to get:
$$1- frac{-x(i-1)-1}{x^2+1}$$
Once again, i'm not sure if this is the correct path.
Some help would be appreciated.
Thanks
polynomials complex-numbers
asked Nov 23 at 13:34
Bucephalus
660417
1
Why do you need to alter the expression? It's already quite short ...
– Matti P.
Nov 23 at 13:36
Try multiplying by $$frac{x+i}{x+i}$$.
– MJD
Nov 23 at 13:38
@MattiP well the book is asking this: "use synthetic division to determine the quotient involving a complex number" and this is the first one of five to do.
– Bucephalus
Nov 23 at 13:42
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given this
$dfrac{x+1}{x-i}$
What can I do with that?
If i do polynomial division as below, I get:
$$x-i)overline{x+1} = 1 + frac{1+i}{x-1}$$
however, I'm not even sure if this is legal maths.
The other thing I think I could to is remove the complex demoninator with the complex conjugate to get:
$$dfrac{x^2-x(i-1)-i}{x^2+1}$$
but I do not know what to do with this from this point on. I tried polynomial division to get:
$$1- frac{-x(i-1)-1}{x^2+1}$$
Once again, i'm not sure if this is the correct path.
Some help would be appreciated.
Thanks
polynomials complex-numbers
asked Nov 23 at 13:34
Bucephalus
660417
Given this
$dfrac{x+1}{x-i}$
What can I do with that?
If i do polynomial division as below, I get:
$$x-i)overline{x+1} = 1 + frac{1+i}{x-1}$$
however, I'm not even sure if this is legal maths.
The other thing I think I could to is remove the complex demoninator with the complex conjugate to get:
$$dfrac{x^2-x(i-1)-i}{x^2+1}$$
but I do not know what to do with this from this point on. I tried polynomial division to get:
$$1- frac{-x(i-1)-1}{x^2+1}$$
Once again, i'm not sure if this is the correct path.
Some help would be appreciated.
Thanks
polynomials complex-numbers
polynomials complex-numbers
asked Nov 23 at 13:34
Bucephalus
660417
asked Nov 23 at 13:34
Bucephalus
660417
asked Nov 23 at 13:34
Bucephalus
660417
asked Nov 23 at 13:34
Bucephalus
660417
asked Nov 23 at 13:34
Bucephalus
660417
660417
1
Why do you need to alter the expression? It's already quite short ...
– Matti P.
Nov 23 at 13:36
Try multiplying by $$frac{x+i}{x+i}$$.
– MJD
Nov 23 at 13:38
@MattiP well the book is asking this: "use synthetic division to determine the quotient involving a complex number" and this is the first one of five to do.
– Bucephalus
Nov 23 at 13:42
add a comment |
1
Why do you need to alter the expression? It's already quite short ...
– Matti P.
Nov 23 at 13:36
Try multiplying by $$frac{x+i}{x+i}$$.
– MJD
Nov 23 at 13:38
@MattiP well the book is asking this: "use synthetic division to determine the quotient involving a complex number" and this is the first one of five to do.
– Bucephalus
Nov 23 at 13:42
1
1
Why do you need to alter the expression? It's already quite short ...
– Matti P.
Nov 23 at 13:36
Why do you need to alter the expression? It's already quite short ...
– Matti P.
Nov 23 at 13:36
Try multiplying by $$frac{x+i}{x+i}$$.
– MJD
Nov 23 at 13:38
Try multiplying by $$frac{x+i}{x+i}$$.
– MJD
Nov 23 at 13:38
@MattiP well the book is asking this: "use synthetic division to determine the quotient involving a complex number" and this is the first one of five to do.
– Bucephalus
Nov 23 at 13:42
@MattiP well the book is asking this: "use synthetic division to determine the quotient involving a complex number" and this is the first one of five to do.
– Bucephalus
Nov 23 at 13:42
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Polynomial division (quotient and remainder) in ${Bbb C}[x]$ gives
$$x+1 = 1cdot (x-i) + (1+i).$$
answered Nov 23 at 13:37
Wuestenfux
3,0451410
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3010371%2fdivision-involving-a-complex-number%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Polynomial division (quotient and remainder) in ${Bbb C}[x]$ gives
$$x+1 = 1cdot (x-i) + (1+i).$$
answered Nov 23 at 13:37
Wuestenfux
3,0451410
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
add a comment |
up vote
1
down vote
accepted
Polynomial division (quotient and remainder) in ${Bbb C}[x]$ gives
$$x+1 = 1cdot (x-i) + (1+i).$$
answered Nov 23 at 13:37
Wuestenfux
3,0451410
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Polynomial division (quotient and remainder) in ${Bbb C}[x]$ gives
$$x+1 = 1cdot (x-i) + (1+i).$$
answered Nov 23 at 13:37
Wuestenfux
3,0451410
Polynomial division (quotient and remainder) in ${Bbb C}[x]$ gives
$$x+1 = 1cdot (x-i) + (1+i).$$
answered Nov 23 at 13:37
Wuestenfux
3,0451410
answered Nov 23 at 13:37
Wuestenfux
3,0451410
answered Nov 23 at 13:37
Wuestenfux
3,0451410
answered Nov 23 at 13:37
Wuestenfux
3,0451410
3,0451410
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
add a comment |
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
Thanks @Wuestenfux you're answer has pointed out an error in my maths.
– Bucephalus
Nov 23 at 13:46
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3010371%2fdivision-involving-a-complex-number%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
Why do you need to alter the expression? It's already quite short ...
– Matti P.
Nov 23 at 13:36
Try multiplying by $$frac{x+i}{x+i}$$.
– MJD
Nov 23 at 13:38
@MattiP well the book is asking this: "use synthetic division to determine the quotient involving a complex number" and this is the first one of five to do.
– Bucephalus
Nov 23 at 13:42