# Complex Numbers

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 :)

## Answers and Replies

sutupidmath
1 + i = √2(cos π/4+ i sin π/4)

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

Craig :)

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

neutrino
what do these litle squares stand for? what are those symbols, what do they represent??
I'm glad that I'm not the only seeing those squares. Some problem with fonts, I suppose.

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 :)

Homework Helper
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.

Homework Helper
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).

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.

Homework Helper
Yup what neutrino said :D

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 