What is $max(|z|)$ if $Bigl|frac6z - i2 + 3izBigr|leq1$Understanding why $int_0^pi/2 sqrt1+cos^2x geq fracpi4bigl( 1 + sqrt2bigr)$Calculate $Bigl|frac1n^zBigr|$.Show that $Pleft(limsuplimits_ttoinftyleft|B_tright|/t>cright)leq Pleft(suplimits_tin[n,n+1]left|B_tright|/n>c;mboxi.o.right)$Why is my solution incorrect? AM GM inequalityComplex numbers $left(frac1+i1-iright)^k = 1$ what is $k$?What are the points of differentiability of $f(z)=vert z vert^2+iota bar z +1$?Verification involving modulus and complex numbersEquality occurring at two different values for a three way inequalityProof for Floor function exponent algebra IdentityReverse Littlewood-Offord problem: lower bound for the number of choices of signs such that $|pm a_1dotspm a_n| leq max|a_i|.$
Happy pi day, everyone!
What's the meaning of a knight fighting a snail in medieval book illustrations?
How are passwords stolen from companies if they only store hashes?
Official degrees of earth’s rotation per day
Why is a white electrical wire connected to 2 black wires?
How should I state my peer review experience in the CV?
Bacteria contamination inside a thermos bottle
Fastest way to pop N items from a large dict
Is there a hypothetical scenario that would make Earth uninhabitable for humans, but not for (the majority of) other animals?
How to terminate ping <dest> &
Violin - Can double stops be played when the strings are not next to each other?
Is there a place to find the pricing for things not mentioned in the PHB? (non-magical)
Recruiter wants very extensive technical details about all of my previous work
How do I hide Chekhov's Gun?
Is there a symmetric-key algorithm which we can use for creating a signature?
How do I change two letters closest to a string and one letter immediately after a string using Notepad++?
How could an airship be repaired midflight?
Instead of a Universal Basic Income program, why not implement a "Universal Basic Needs" program?
Brexit - No Deal Rejection
Why is the President allowed to veto a cancellation of emergency powers?
Is it good practice to use Linear Least-Squares with SMA?
What is the Japanese sound word for the clinking of money?
Can I use USB data pins as power source
Why does a Star of David appear at a rally with Francisco Franco?
What is $max(|z|)$ if $Bigl|frac6z - i2 + 3izBigr|leq1$
Understanding why $int_0^pi/2 sqrt1+cos^2x geq fracpi4bigl( 1 + sqrt2bigr)$Calculate $Bigl|frac1n^zBigr|$.Show that $Pleft(limsuplimits_ttoinftyleft|B_tright|/t>cright)leq Pleft(suplimits_tin[n,n+1]left|B_tright|/n>c;mboxi.o.right)$Why is my solution incorrect? AM GM inequalityComplex numbers $left(frac1+i1-iright)^k = 1$ what is $k$?What are the points of differentiability of $f(z)=vert z vert^2+iota bar z +1$?Verification involving modulus and complex numbersEquality occurring at two different values for a three way inequalityProof for Floor function exponent algebra IdentityReverse Littlewood-Offord problem: lower bound for the number of choices of signs such that $|pm a_1dotspm a_n| leq max|a_i|.$
$begingroup$
I'm solving a multiple choice question but my answer is not among the choices and I don't know where I am wrong. The question is this:
What is the $max|z|$ if: $$Bigl|frac6z - i2 + 3izBigr|leq1$$ and $z$ is a complex number.
- $frac15$
- $frac14$
- $frac13$
- $frac12$
My solution is this but my answer isn't among them:
$$ biggl|frac6z - i2 + 3izbiggr|leq1Rightarrow |6z-i| leq |2+3iz| Rightarrow |6z-i|^2 leq |2+3iz|^2 $$
$$ Rightarrow (6z-i)overline(6z-i) leq (2+3iz)overline(2+3iz) $$
$$ Rightarrow (6z-i)(6barz+i) leq (2+3iz)(2-3ibarz) $$
$$ Rightarrow 36|z|^2 +6iz - 6ibarz + 1 leq 4 - 6ibarz +6iz + 9|z|^2 $$
$$ Rightarrow 17|z|^2 leq 3 Rightarrow |z|^2 leq frac317 Rightarrow |z| leq sqrtfrac317$$
Where am I wrong? what is the right solution?
Thanks in advance.
inequality complex-numbers
edited Mar 12 at 11:08
Bernard
123k741116
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
$endgroup$
add a comment |
$begingroup$
I'm solving a multiple choice question but my answer is not among the choices and I don't know where I am wrong. The question is this:
What is the $max|z|$ if: $$Bigl|frac6z - i2 + 3izBigr|leq1$$ and $z$ is a complex number.
- $frac15$
- $frac14$
- $frac13$
- $frac12$
My solution is this but my answer isn't among them:
$$ biggl|frac6z - i2 + 3izbiggr|leq1Rightarrow |6z-i| leq |2+3iz| Rightarrow |6z-i|^2 leq |2+3iz|^2 $$
$$ Rightarrow (6z-i)overline(6z-i) leq (2+3iz)overline(2+3iz) $$
$$ Rightarrow (6z-i)(6barz+i) leq (2+3iz)(2-3ibarz) $$
$$ Rightarrow 36|z|^2 +6iz - 6ibarz + 1 leq 4 - 6ibarz +6iz + 9|z|^2 $$
$$ Rightarrow 17|z|^2 leq 3 Rightarrow |z|^2 leq frac317 Rightarrow |z| leq sqrtfrac317$$
Where am I wrong? what is the right solution?
Thanks in advance.
inequality complex-numbers
edited Mar 12 at 11:08
Bernard
123k741116
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
$endgroup$
add a comment |
$begingroup$
I'm solving a multiple choice question but my answer is not among the choices and I don't know where I am wrong. The question is this:
What is the $max|z|$ if: $$Bigl|frac6z - i2 + 3izBigr|leq1$$ and $z$ is a complex number.
- $frac15$
- $frac14$
- $frac13$
- $frac12$
My solution is this but my answer isn't among them:
$$ biggl|frac6z - i2 + 3izbiggr|leq1Rightarrow |6z-i| leq |2+3iz| Rightarrow |6z-i|^2 leq |2+3iz|^2 $$
$$ Rightarrow (6z-i)overline(6z-i) leq (2+3iz)overline(2+3iz) $$
$$ Rightarrow (6z-i)(6barz+i) leq (2+3iz)(2-3ibarz) $$
$$ Rightarrow 36|z|^2 +6iz - 6ibarz + 1 leq 4 - 6ibarz +6iz + 9|z|^2 $$
$$ Rightarrow 17|z|^2 leq 3 Rightarrow |z|^2 leq frac317 Rightarrow |z| leq sqrtfrac317$$
Where am I wrong? what is the right solution?
Thanks in advance.
inequality complex-numbers
edited Mar 12 at 11:08
Bernard
123k741116
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
$endgroup$
I'm solving a multiple choice question but my answer is not among the choices and I don't know where I am wrong. The question is this:
What is the $max|z|$ if: $$Bigl|frac6z - i2 + 3izBigr|leq1$$ and $z$ is a complex number.
- $frac15$
- $frac14$
- $frac13$
- $frac12$
My solution is this but my answer isn't among them:
$$ biggl|frac6z - i2 + 3izbiggr|leq1Rightarrow |6z-i| leq |2+3iz| Rightarrow |6z-i|^2 leq |2+3iz|^2 $$
$$ Rightarrow (6z-i)overline(6z-i) leq (2+3iz)overline(2+3iz) $$
$$ Rightarrow (6z-i)(6barz+i) leq (2+3iz)(2-3ibarz) $$
$$ Rightarrow 36|z|^2 +6iz - 6ibarz + 1 leq 4 - 6ibarz +6iz + 9|z|^2 $$
$$ Rightarrow 17|z|^2 leq 3 Rightarrow |z|^2 leq frac317 Rightarrow |z| leq sqrtfrac317$$
Where am I wrong? what is the right solution?
Thanks in advance.
inequality complex-numbers
inequality complex-numbers
edited Mar 12 at 11:08
Bernard
123k741116
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
edited Mar 12 at 11:08
Bernard
123k741116
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
edited Mar 12 at 11:08
Bernard
123k741116
edited Mar 12 at 11:08
Bernard
123k741116
edited Mar 12 at 11:08
Bernard
123k741116
123k741116
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
asked Mar 12 at 9:38
Peyman mohseni kiasariPeyman mohseni kiasari
12811
12811
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$36-9=27$. You have taken it as $17$. The correct answer is 3).
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
$endgroup$
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',
autoActivateHeartbeat: false,
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%2f3144873%2fwhat-is-maxz-if-bigl-frac6z-i2-3iz-bigr-leq1%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
$begingroup$
$36-9=27$. You have taken it as $17$. The correct answer is 3).
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
$endgroup$
add a comment |
$begingroup$
$36-9=27$. You have taken it as $17$. The correct answer is 3).
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
$endgroup$
add a comment |
$begingroup$
$36-9=27$. You have taken it as $17$. The correct answer is 3).
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
$endgroup$
$36-9=27$. You have taken it as $17$. The correct answer is 3).
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
answered Mar 12 at 9:42
Kavi Rama MurthyKavi Rama Murthy
67.6k53067
67.6k53067
add a comment |
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.
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%2f3144873%2fwhat-is-maxz-if-bigl-frac6z-i2-3iz-bigr-leq1%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
