# 2e^5i in rectangular form?

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I hear of the e^ia = (-1)^a/pi

But I'm not sure what -1^5/pi has in relation to 2e^5 like, is there a relation on polar coordinates that I'm missing to I somehow get this in the form:

x + yi by rearranging?

But I'm not sure what -1^5/pi has in relation to 2e^5 like, is there a relation on polar coordinates that I'm missing to I somehow get this in the form:

x + yi by rearranging?

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#2

It can be obtained from that:

so

where for a complex value: where a and b are real values:

(can be seen as the norm of z),

x is the argument of z (the angle z makes with the positive real axis).

--------------------------------------------------------------------------------------

So in effect a complex value z has three forms (not including z=0).

Does that clear up a few things?

so

where for a complex value: where a and b are real values:

(can be seen as the norm of z),

x is the argument of z (the angle z makes with the positive real axis).

--------------------------------------------------------------------------------------

So in effect a complex value z has three forms (not including z=0).

Does that clear up a few things?

Last edited by simon0; 6 months ago

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(Original post by

It can be obtained from that:

so

where for a complex value: where a and b are real values:

(can be seen as the norm of z),

x is the argument of z (the angle z makes with the positive real axis).

--------------------------------------------------------------------------------------

Does that clear up a few things?

**simon0**)It can be obtained from that:

so

where for a complex value: where a and b are real values:

(can be seen as the norm of z),

x is the argument of z (the angle z makes with the positive real axis).

--------------------------------------------------------------------------------------

Does that clear up a few things?

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OK but that, forgive me if I'm wrong ends in polar form and somes from a simple complex number of a + ib.

How the hell do I apply that to this question?????

Cartesian form is required, I just dont know how to get it from an exponential as it is a whole equation unto itself.

How the hell do I apply that to this question?????

Cartesian form is required, I just dont know how to get it from an exponential as it is a whole equation unto itself.

Last edited by NeedABtterUserID; 6 months ago

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#6

(Original post by

so are is the coefficient (in my case 2) but how does the ix collapse into separate cos and sin?

**NeedABtterUserID**)so are is the coefficient (in my case 2) but how does the ix collapse into separate cos and sin?

Then you can separate the terms to obtain the Taylor expansion for sin(x) and icos(x).

This is well done from website:

https://socratic.org/questions/how-d...-ix-cosx-isinx

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(Original post by

One way is to use the Taylor expansion of the exponential with "ix" as the argument.

Then you can separate the terms to obtain the Taylor expansion for sin(x) and icos(x).

This is well done from website:

https://socratic.org/questions/how-d...-ix-cosx-isinx

**simon0**)One way is to use the Taylor expansion of the exponential with "ix" as the argument.

Then you can separate the terms to obtain the Taylor expansion for sin(x) and icos(x).

This is well done from website:

https://socratic.org/questions/how-d...-ix-cosx-isinx

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#8

(Original post by

OK but that, forgive me if I'm wrong ends in polar form and somes from a simple complex number of a + ib.

How the hell do I apply that to this question?????

Cartesian form is required, I just dont know how to get it from an exponential as it is a whole equation unto itself.

**NeedABtterUserID**)OK but that, forgive me if I'm wrong ends in polar form and somes from a simple complex number of a + ib.

How the hell do I apply that to this question?????

Cartesian form is required, I just dont know how to get it from an exponential as it is a whole equation unto itself.

Of your last line, it looks like you want to go from the exponential form to the Cartesian form.

Just use the formula I gave earlier:

For example:

Is that okay?

Last edited by simon0; 6 months ago

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(Original post by

I do not understand the first two lines of your reply.

Of your last line, it looks like you want to go from the exponential form to the Cartesian form.

Just use the formula I gave earlier:

For example:

Is that okay?

**simon0**)I do not understand the first two lines of your reply.

Of your last line, it looks like you want to go from the exponential form to the Cartesian form.

Just use the formula I gave earlier:

For example:

Is that okay?

May I just verify I have this right:

For my case I have Re^ix where x is a whole number not a multiple or division of pi, does this mean that I would plug a whole number into my sin and cos?

This just seems strange because the number is quite high its 19. (the real equation is 25/27e^19i (I wanted to understand not just steal answers)) but this would suggest multiple rotations around the origin, do I just divide by pi and take the remainder?

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#10

(Original post by

I think I understand now, thanks a million!

May I just verify I have this right:

For my case I have Re^ix where x is a whole number not a multiple or division of pi, does this mean that I would plug a whole number into my sin and cos?

This just seems strange because the number is quite high its 19. (the real equation is 25/27e^19i (I wanted to understand not just steal answers)) but this would suggest multiple rotations around the origin, do I just divide by pi and take the remainder?

**NeedABtterUserID**)I think I understand now, thanks a million!

May I just verify I have this right:

For my case I have Re^ix where x is a whole number not a multiple or division of pi, does this mean that I would plug a whole number into my sin and cos?

This just seems strange because the number is quite high its 19. (the real equation is 25/27e^19i (I wanted to understand not just steal answers)) but this would suggest multiple rotations around the origin, do I just divide by pi and take the remainder?

19 seems high but is valid but substitute as usual (then afterwards we can find the argument/x value which is between to which this x-value is better known as the "Principal Argument" but we are getting ahead here).

You are correct it does mean multiple rotations around the origin.

Fun fact:

As all complex values (except 0) can have various representations for example:

where k is an integer, as each rotaion of gets us back to the same position in the argand diagram.

So 1 is .

Last edited by simon0; 6 months ago

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