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How do I solve this to represent the complex number in Cartesian coordinate
Cartesian and Polar Coordinaterepresent real number as case of complex numberHow to solve complex numberHow to solve $|z^2-1|<|z|^2$ where $z$ is a complex number?Complex Number on Cartesian Coordinate System QuestionExpress a complex number in the Cartesian formConverting Complex numbers into Cartesian FormNumber of solution(s) of a complex equationRaising complex number to high power - Cartesian formHow to add real number and complex number in polar form
$begingroup$
How do I solve this to represent the complex number in Cartesian coordinate
$$z=frace^fracpi3ie^frac23pi icdot 2e^fracpi6i$$
So I got this question as a homework and I am not able to solve it correctly. Any leads on how to solve this would help.
complex-numbers exponential-function
edited Apr 5 at 17:54
blub
3,289929
asked Apr 5 at 17:47
ardentcoderardentcoder
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
How do I solve this to represent the complex number in Cartesian coordinate
$$z=frace^fracpi3ie^frac23pi icdot 2e^fracpi6i$$
So I got this question as a homework and I am not able to solve it correctly. Any leads on how to solve this would help.
complex-numbers exponential-function
edited Apr 5 at 17:54
blub
3,289929
asked Apr 5 at 17:47
ardentcoderardentcoder
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
What do you want to solve ?
$endgroup$
– blub
Apr 5 at 17:48
$begingroup$
The image link is given
$endgroup$
– ardentcoder
Apr 5 at 17:48
$begingroup$
Don't use links in your question and rather make the effort to type it using MathJax.
$endgroup$
– blub
Apr 5 at 17:52
$begingroup$
Sorry about that. Will use it from next time. New to stack exchange mathematics.
$endgroup$
– ardentcoder
Apr 5 at 17:53
add a comment |
$begingroup$
How do I solve this to represent the complex number in Cartesian coordinate
$$z=frace^fracpi3ie^frac23pi icdot 2e^fracpi6i$$
So I got this question as a homework and I am not able to solve it correctly. Any leads on how to solve this would help.
complex-numbers exponential-function
edited Apr 5 at 17:54
blub
3,289929
asked Apr 5 at 17:47
ardentcoderardentcoder
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
How do I solve this to represent the complex number in Cartesian coordinate
$$z=frace^fracpi3ie^frac23pi icdot 2e^fracpi6i$$
So I got this question as a homework and I am not able to solve it correctly. Any leads on how to solve this would help.
complex-numbers exponential-function
complex-numbers exponential-function
edited Apr 5 at 17:54
blub
3,289929
asked Apr 5 at 17:47
ardentcoderardentcoder
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 5 at 17:54
blub
3,289929
asked Apr 5 at 17:47
ardentcoderardentcoder
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 5 at 17:54
blub
3,289929
edited Apr 5 at 17:54
blub
3,289929
edited Apr 5 at 17:54
blub
3,289929
3,289929
asked Apr 5 at 17:47
ardentcoderardentcoder
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 5 at 17:47
ardentcoderardentcoder
84
asked Apr 5 at 17:47
ardentcoderardentcoder
84
84
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
ardentcoder is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
What do you want to solve ?
$endgroup$
– blub
Apr 5 at 17:48
$begingroup$
The image link is given
$endgroup$
– ardentcoder
Apr 5 at 17:48
$begingroup$
Don't use links in your question and rather make the effort to type it using MathJax.
$endgroup$
– blub
Apr 5 at 17:52
$begingroup$
Sorry about that. Will use it from next time. New to stack exchange mathematics.
$endgroup$
– ardentcoder
Apr 5 at 17:53
add a comment |
$begingroup$
What do you want to solve ?
$endgroup$
– blub
Apr 5 at 17:48
$begingroup$
The image link is given
$endgroup$
– ardentcoder
Apr 5 at 17:48
$begingroup$
Don't use links in your question and rather make the effort to type it using MathJax.
$endgroup$
– blub
Apr 5 at 17:52
$begingroup$
Sorry about that. Will use it from next time. New to stack exchange mathematics.
$endgroup$
– ardentcoder
Apr 5 at 17:53
$begingroup$
What do you want to solve ?
$endgroup$
– blub
Apr 5 at 17:48
$begingroup$
What do you want to solve ?
$endgroup$
– blub
Apr 5 at 17:48
$begingroup$
The image link is given
$endgroup$
– ardentcoder
Apr 5 at 17:48
$begingroup$
The image link is given
$endgroup$
– ardentcoder
Apr 5 at 17:48
$begingroup$
Don't use links in your question and rather make the effort to type it using MathJax.
$endgroup$
– blub
Apr 5 at 17:52
$begingroup$
Don't use links in your question and rather make the effort to type it using MathJax.
$endgroup$
– blub
Apr 5 at 17:52
$begingroup$
Sorry about that. Will use it from next time. New to stack exchange mathematics.
$endgroup$
– ardentcoder
Apr 5 at 17:53
$begingroup$
Sorry about that. Will use it from next time. New to stack exchange mathematics.
$endgroup$
– ardentcoder
Apr 5 at 17:53
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: For any $xinmathbb R$, you have
$$e^ix=cos(x)+isin(x)$$
also known as Euler's formula.
So, e.g. considering $e^fracpi3i$, as $pi/3inmathbb R$, we have
$$e^fracpi3i=cos(pi/3)+isin(pi/3)=frac12+ifracsqrt32$$
You can proceed to use this conversion of polar to cartesian representations to convert the other expressions. Then, you may proceed to do arithmetic on those cartesian-represented numbers as usual.
answered Apr 5 at 17:51
blubblub
3,289929
$endgroup$
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
add a comment |
Your Answer
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1 Answer
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oldest
votes
1 Answer
1
active
oldest
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active
oldest
votes
active
oldest
votes
$begingroup$
Hint: For any $xinmathbb R$, you have
$$e^ix=cos(x)+isin(x)$$
also known as Euler's formula.
So, e.g. considering $e^fracpi3i$, as $pi/3inmathbb R$, we have
$$e^fracpi3i=cos(pi/3)+isin(pi/3)=frac12+ifracsqrt32$$
You can proceed to use this conversion of polar to cartesian representations to convert the other expressions. Then, you may proceed to do arithmetic on those cartesian-represented numbers as usual.
answered Apr 5 at 17:51
blubblub
3,289929
$endgroup$
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
add a comment |
$begingroup$
Hint: For any $xinmathbb R$, you have
$$e^ix=cos(x)+isin(x)$$
also known as Euler's formula.
So, e.g. considering $e^fracpi3i$, as $pi/3inmathbb R$, we have
$$e^fracpi3i=cos(pi/3)+isin(pi/3)=frac12+ifracsqrt32$$
You can proceed to use this conversion of polar to cartesian representations to convert the other expressions. Then, you may proceed to do arithmetic on those cartesian-represented numbers as usual.
answered Apr 5 at 17:51
blubblub
3,289929
$endgroup$
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
add a comment |
$begingroup$
Hint: For any $xinmathbb R$, you have
$$e^ix=cos(x)+isin(x)$$
also known as Euler's formula.
So, e.g. considering $e^fracpi3i$, as $pi/3inmathbb R$, we have
$$e^fracpi3i=cos(pi/3)+isin(pi/3)=frac12+ifracsqrt32$$
You can proceed to use this conversion of polar to cartesian representations to convert the other expressions. Then, you may proceed to do arithmetic on those cartesian-represented numbers as usual.
answered Apr 5 at 17:51
blubblub
3,289929
$endgroup$
Hint: For any $xinmathbb R$, you have
$$e^ix=cos(x)+isin(x)$$
also known as Euler's formula.
So, e.g. considering $e^fracpi3i$, as $pi/3inmathbb R$, we have
$$e^fracpi3i=cos(pi/3)+isin(pi/3)=frac12+ifracsqrt32$$
You can proceed to use this conversion of polar to cartesian representations to convert the other expressions. Then, you may proceed to do arithmetic on those cartesian-represented numbers as usual.
answered Apr 5 at 17:51
blubblub
3,289929
edited Apr 5 at 18:04
answered Apr 5 at 17:51
blubblub
3,289929
answered Apr 5 at 17:51
blubblub
3,289929
answered Apr 5 at 17:51
blubblub
3,289929
3,289929
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
add a comment |
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
Yes I saw this equation online. So i have to use this and solve the equation first and represent in cartesian coordinate?
$endgroup$
– ardentcoder
Apr 5 at 18:00
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
@ardentcoder I'll edit my answer.
$endgroup$
– blub
Apr 5 at 18:01
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
$begingroup$
Thank you . Will proceed with this.
$endgroup$
– ardentcoder
Apr 5 at 18:33
add a comment |
ardentcoder is a new contributor. Be nice, and check out our Code of Conduct.
ardentcoder is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
What do you want to solve ?
$endgroup$
– blub
Apr 5 at 17:48
$begingroup$
The image link is given
$endgroup$
– ardentcoder
Apr 5 at 17:48
$begingroup$
Don't use links in your question and rather make the effort to type it using MathJax.
$endgroup$
– blub
Apr 5 at 17:52
$begingroup$
Sorry about that. Will use it from next time. New to stack exchange mathematics.
$endgroup$
– ardentcoder
Apr 5 at 17:53