# J-Notation (Complex Numbers)

1. Jan 22, 2007

Firstly I do apologise, because this question is got more to do with the mathematical side of Electronic Engineering, because my mathematical classification is not that good I don't know where I would put this question on the mathematics section, if any of the moderators or whoever can, wants to move it there, I do apologise.

I am having a bit of problem with my calculator, unlike many other people in my class, my calculator can't exchange complex numbers to polar form, so I have to do it by using some mathematics.

I know how to change from polar form back to complex notation, so for example imagine a voltage of 6.08 |51.8*.

I believe that 6.08cos51.8 will get you the real component and 6.08sin51.8 is J, so in J-notation ==> 6.08 |51.8* = 3.76 + J4.78

I haven't made up these difficult numbers, but I have taken them from a class example, I suppose the method is correct because that was the answer checked by the teacher.

However I do not know how to exchange a number back to polar form, I think my best option would be buying a better calculator, but I would appreciate if someone could show me by mathematical terms, Thank You.

2. Jan 22, 2007

### cristo

Staff Emeritus
Let's consider a general case first, and consider the complex number x+yj, where x and y are real numbers. Now, we want to express this in polar form, which is R(cost+jsint). Here, R is the modulus of the complex number (I'm not sure whether you're familiar with this) but it is simply defined as √(x2+y2).

So, to move onto your example, we want to write 3.76+4.78j in the form R(cost+jsint). First calculate the modulus of the complex number; R=√(3.762+4.782)=6.08. Now, we factor this out of the complex number, to give 6.08(0.6181+0.7026j). This is nearly in polar form. The final step is to take cos-1(0.6181) and sin-1(0.7026). You will find that these are both 51.8, and so we have the number expressed as 6.08(cos(51.8)+jsin(51.8)), which has real part 6.08cos(51.8) and imaginary part 6.08sin(51.8), as you state in your post.

Hope this helps!

Last edited: Jan 22, 2007
3. Jan 22, 2007

### Staff: Mentor

No worries, I googled polar to rectangular conversion complex numbers, and got lots of good hits. Here's the first one:

Basically just think of the trigonometry involved, with an x-y graph where the +x axis is the Real axis, and the +y axis is the Imaginary axis. We use the prefex j (or i in non-EE areas) to denote the Imaginary component in the rectangular form of complex numbers, or as a prefex to the angle (in radians) in complex exponential form (which is another notation for the polar form).

4. Jan 22, 2007

### Staff: Mentor

Dang, cristo beats me to the punch again!!

5. Jan 22, 2007