# math: polar form addition

#### P-MONKE

Joined Mar 14, 2012
83

#### omaroski

Joined Jun 19, 2008
34
You mean applying Pythagorean Theorem to find the hypotenuse? $\sqrt{10^2+6^2}$

if i'm not wrog that would be if numbers are at 0° and 90°

in fact i would get 11,66 in place of 14.861 as in the example.

#### crutschow

Joined Mar 14, 2008
23,155
The answer will be : 16 V < 45o
No. If you look at the reference listed you will see that that answer is 14.861V < 16.59°.

You add the two by first converting from polar to rectangular form:

10 <0° = 10 +j0
6 <45° = 4.24 + j4.24

Then you add the rectangular values:

(10 +j0) +(4.24 + j4.24) = 14.24 +j4.24

Then you convert this back to polar form:

14.24 +j4.24 = 14.86 <16.59°

#### P-MONKE

Joined Mar 14, 2012
83
Awww - you beat me to it

I was just doing this longhand to show all the steps, as a few posters didn't seem to grasp the concept.

It was good practice for me though, as I'm very rusty.

I'm going to post it anyway because I made the effort

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#### omaroski

Joined Jun 19, 2008
34
I read the chapter on complex numbers more accurately and found it.

I couldn't understand why there was multiplication, divison and inversion of polar numbers while no addition and subtraction. Then saw it was necessary convert to rectangular form using cos e sin functions, do the addition and convert to polar back again obviously.

Thank you for your efforts!

#### omaroski

Joined Jun 19, 2008
34

i was calculating sin and cos with electronic calculator and with 45° i noticed that it's nothing but 1/√2 both. What's the point so?

#### crutschow

Joined Mar 14, 2008
23,155

i was calculating sin and cos with electronic calculator and with 45° i noticed that it's nothing but 1/√2 both. What's the point so?
The sin and cos of 45° are the same. Thats because a 45° right-angle triangle has two equal sides. So what's your question?

#### omaroski

Joined Jun 19, 2008
34
The sin and cos of 45° are the same. Thats because a 45° right-angle triangle has two equal sides. So what's your question?
The one you replied!

It's not my field, trigonometry i mean. I couldn't tell what a sine and cosine functions would describe exactly!

#### P-MONKE

Joined Mar 14, 2012
83
The one you replied!

It's not my field, trigonometry i mean. I couldn't tell what a sine and cosine functions would describe exactly!
They are all about "squaring the circle"

BTW, I used "i" for the complex component, something at the back of my mind tells me that "j" (as used by crutschow) is more commonly used in electrical and electronic formulae.
"i" tends to be used more by mathematicians, I believe.

#### crutschow

Joined Mar 14, 2008
23,155
Here's a short primer on trig.

The reason trig is used for AC circuit calculations is that the 90° phase angle between current and voltage caused by reactive components can be viewed as two vectors with a 90° angle. Then the sum of these vectors can be solved by viewing them as the sides of a right triangle with the hypotenuse length and angle being the sum of the two vectors.

Thus the hypotenuse length and angle is the polar form of value and the length of the sides is the rectangular form (with the "j" component being the vertical side).

#### WBahn

Joined Mar 31, 2012
24,576
Forgive me for pulling up a somewhat moldy thread, but this highlights a real problem with technical education (and I don't think it knows much in the way of national borders, meaning that no country is immune). We are increasingly the victims of our own technological success. We have calculators that give you sin() and cos() by punching a button and so students are taught that when you see a formula with sin() or cos() that you first punch the buttons for what's inside the parentheses, then you punch the button that says sin' or 'cos' on it. I've seen trig textbooks here that spend far more time giving illustrated examples of which buttons to press on the calculator than covering the concepts and how to work with them. The same for exponentials and logarithms. It hit me in the face when I had two extremely bright students, both of whom had been their respective high school valedictorians and both had gotten A's in AP math, come up after class because they couldn't understand the step on the board in which I had:

e^ln(z) = z

It took only a couple of minutes to explain the fundamental inverse relationship between the two and they understood it perfectly. But both said that, up to that point, they had only been taught that exponentials and logarithms were functions, just like the trig functions, that you would see from time to time in formulas and to evaluate the expression you push these buttons on your calculator.

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