# rectangular to polar conversions

Discussion in 'General Electronics Chat' started by lemon, Jan 2, 2012.

1. ### lemon Thread Starter Member

Jan 28, 2010
125
2
Hi:
I am reading/working through the following page on ac Series-parallel R, L, and C circuits. On this page they make a conversion from rectangular to polar forms but I am having difficulty understanding how they came to the eventual polar angles. I am ok with doing basic conversions. Could someone explain that for me please, or direct me to the page that does. I read it somewhere on these pages earlier but can't recall it and can't seem to find it now. Thank you.

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Dec 5, 2007
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3. ### lemon Thread Starter Member

Jan 28, 2010
125
2
yeah I have studied that page before but am still confused. The thing that is confusing me is that in the conversion from rectangular form to polar form, we use arctan(b/a), which for the first example in the attached image, Zc1=0-j564.38, would be arctan(564.38/0), which is of course undefined. Yet their solution is 564.38<-90.

4. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
The tan of 90 degrees is not undefined it is infinite; so the arctan of infinity is 90 degrees and the arctan of minus infinity is -90 degrees.

Undefined is something 0/0

Plot the points on the complex plane to see what is going on.

5. ### lemon Thread Starter Member

Jan 28, 2010
125
2
The tan of 90 degrees is not undefined it is infinite; so the arctan of infinity is 90 degrees and the arctan of minus infinity is -90 degrees.

Undefined is something 0/0

Understood.
But - 564.38 on the complex plane puts it in the lower left quadrant. While that is minus, it isn't -90. Isn't is -155.62?

6. ### t06afre AAC Fanatic!

May 11, 2009
5,939
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Take a look at this picture. The Y axis is equal to the j axis

7. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
No that is not correct. The complex number has two(2) components, just like a vector. 0 - j564.38 has a Real part of 0 so you stay on the vertical axis and you go 564.38 units in the negative j (aka y) direction and you arrive at the point (0, -564.38) in Cartesian coordinates which is equivalent to the the complex number 0 -j564.38 on the complex plane. Got it now?

lemon likes this.
8. ### lemon Thread Starter Member

Jan 28, 2010
125
2
yep! I think so. I don't go round I go up and down and left and right

But that is only when there is a zero involved though, right?

Last edited: Jan 7, 2012

Feb 24, 2006
10,340
1,850
Yes, Right

10. ### lemon Thread Starter Member

Jan 28, 2010
125
2
Cool - I've got it - thank you