# Complex Numbers

1. Apr 13, 2007

### craig100

Hello guys;
I'm after a bit of help here, I may have missed something completely obvious, but I can't seem to figure out the working of:

1 + i = √2(cos π/4+ i sin π/4)

ie; How does 1 + i equal √2(cos π/4+ i sin π/4)??

any help would be appreciated;
Thanks
Craig :)

2. Apr 13, 2007

### sutupidmath

what do these litle squares stand for? what are those symbols, what do they represent??

3. Apr 13, 2007

### neutrino

I'm glad that I'm not the only seeing those squares. Some problem with fonts, I suppose.

4. Apr 13, 2007

### craig100

Sorry, I guess you don't have those fonts installed on your system...i'll put it a different way;

1 + i = root(2) . (cos(pi/4) + i.sin(pi/4))

pi ...being pi(3.14...) :P

so my question is how does (1 + i) equal the value above?

I hope thats clearer?

Craig :)

5. Apr 13, 2007

### Gib Z

Any complex number can be expressed in the form a+bi.

In this case, a=1 and b=1.
Complex numbers can be expressed in the following form:
$$r(\cos x + i\sin x)$$ where $r=\sqrt{a^2+b^2}$ and x is arctan (b/a). Anything you don't understand or want more info on im right here.

6. Apr 13, 2007

### Gib Z

Ok picture a plane where one unit on the y axis is 1 unit on the imaginaries, or x units "up" is xi. And the x axis is just the real number line. So to denote a+bi, we would have a point that is a units from the origin to the right, and b units up. Or co ordinates, (a,b).

7. Apr 13, 2007

### neutrino

Craig,
Plot the complex number on an Argand Plane. Find it's real and imaginary components in terms of the angle it makes with the real axis, and it's modulus.

8. Apr 13, 2007

### Gib Z

Yup what neutrino said :D

9. Apr 13, 2007

### craig100

ahh, thanks guys...its been a while since I have done complex numbers, I understand it now , thanks for the quick and informative replies.

Craig