Solving Complex Numbers: How Does 1 + i Equal √2?

[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 :)

 

[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 that's clearer?

Craig :)

 

[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 I am right here.

 

[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).

 

[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.

 

[Gib Z]

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