Exponential Form of Complex Number

[Naz]

Hello I was working through a download of Stroud Engineering Maths 1st edition to teach myself about Complex Numbers, and I did one of the Test Exercises and I realise there is something I do not understand (it happens a lot!).

The question says express 10|_37.25 degrees in exponential form and likewise 10|_322.75 degrees.

I know that the exponential form is re^j.theta where the angle is expressed in radians.

I get the first question. The answer is 10e^j0.65.

I calculated the answer to the second to be 10e^j5.63, however the answer in the text book is 10e^-j0.650.

I can see that this answer just uses the fact that this is a negative angle but why don't I get the same result - the answers should agree?

Thanks!

 

[Deleted member 4993]

Hello I was working through a download of Stroud Engineering Maths 1st edition to teach myself about Complex Numbers, and I did one of the Test Exercises and I realise there is something I do not understand (it happens a lot!).

The question says express 10|_37.25 degrees in exponential form and likewise 10|_322.75 degrees.

I know that the exponential form is re^j.theta where the angle is expressed in radians.

I get the first question. The answer is 10e^j0.65.

I calculated the answer to the second to be 10e^j5.63, however the answer in the text book is 10e^-j0.650.

I can see that this answer just uses the fact that this is a negative angle but why don't I get the same result - the answers should agree?

Thanks!

Hint:

tan(Θ) = -tan(2π - Θ)

 

[Naz]

Hint:

tan(Θ) = -tan(2π - Θ)

Thanks. Still not sure.

I get why the text book answer is right. Negative 37.25 degrees is identical to 322.75 degrees so having already worked out the exponential complex for +37.25 degrees, the easiest solution is to just restate the answer with a negative.

I think your hint related to the equivalence of negative angle to positive angle. But I think I understand that. If they are equivalent, then why doesn't my calculation of theta in terms of the positive angle produce an identical answer?

The anticlockwise angle of 322.75 degrees= 1291/720 . Pi Radians so why can't I just substitute this into the general formula for exponential solution = re^jtheta where theta= 5.633

 

[Naz]

Hint:

tan(Θ) = -tan(2π - Θ)

I tried to reply before but I don't see my reply.

I don't understand. I get the logic of the text book answer: the negative clockwise angle = the anticlockwise angle. Is that what you were hinting at?

However why does it not match my calculation which uses the anticlockwise angle of 322.75 degrees x Pi/180 radians?

Thanks

 

[Deleted member 4993]

Your answer and the book's answer are equivalent (equally correct) - because -

tan(Θ) = -tan(2π - Θ)