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# How to change complex numbers from polar to cartesian form? watch

1. I have some complex number answers. I need to chnage them from polar form('modulus' < 'Argument') to Cartesian form(2+1j).
2. (Original post by MatthewTG)
I have some complex number answers. I need to chnage them from polar form('modulus' < 'Argument' to Cartesian form(2+1j).
You know that so, uh, that's pretty much it.

For example
3. (Original post by Zacken)
You know that so, uh, that's pretty much it.

For example
can you walk through it in baby steps?
4. (Original post by MatthewTG)
can you walk through it in baby steps?
Are you doing FP1 or FP2?
5. (Original post by MatthewTG)
can you walk through it in baby steps?
Sorry, I'm not sure how much more simpler I can possibly make it... could you perchance tell me which bit do you not understand? Are you unfamiliar with the cos + i sin form?
6. (Original post by MatthewTG)
I have some complex number answers. I need to change them from polar form('modulus' < 'Argument' to Cartesian form(2+1j).
Complex numbers of the form z = a+bj can be expressed in the form , where r=|z| and , it can be shown from Pythagoras' theorem. So just find the modulus and argument of the complex number 2+j and you can express it in polar form.
7. (Original post by NotNotBatman)
Complex numbers of the form z = a+bj can be expressed in the form , where r=|z| and , it can be shown from Pythagoras' theorem. So just find the modulus and argument of the complex number 2+j and you can express it in polar form.
My numbers are:
1.0586 + 0.1677i
0.1677 + 1.0586i
0.4866 - 0.9550i
-0.7579 - 0.7579i
-0.9550 + 0.4866i

Please tell me how to change them from cartesian to polar form
8. (Original post by MatthewTG)
My numbers are:
1.0586 + 0.1677i
0.1677 + 1.0586i
0.4866 - 0.9550i
-0.7579 - 0.7579i
-0.9550 + 0.4866i

Please tell me how to change them from cartesian to polar form
Assume your complex numbers are in the form:
x + yi

Compute:
Modulus = Root(x^2+y^2) = R
Arg = Tan^-1(y/x) (Tan^-1 for arctan/tan inverse)

Then put it in the form R((cos(arg)+isin(arg))
9. (Original post by Hayytch)
Assume your complex numbers are in the form:
x + yi

Compute:
Modulus = Root(x^2+y^2) = R
Arg = Tan^-1(y/x) (Tan^-1 for arctan/tan inverse)

Then put it in the form R((cos(arg)+isin(arg))
Note that because arctan(x/y) = arctan(-x/-y), you need to be aware of what quadrant your point lies in and potentially adjust by +/- pi.

E.g. -1-i gives x=y=-1 and so arctan(x/y) = pi/4 but the argument you actually want is -3pi/4.

Just in case the OP is doing this on a computer: many programmer/languages have a special function that returns the correct argumentt - often it's atan2(x, y).

Most calculators also do rectangular to polar conversion, or at least they did in my day.

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