# Teaching myself trigconfusion

1. Jul 27, 2005

Hi, I'm in the complex numbers section of a trig book, and I'm having trouble intuitively understanding how a number like 3+5i can become (3,5) on the Gaussian coordinate plane...the logic behind it doesn't jump out at me...

Any help?

And is calculus generally a smooth transition after mastering trig and algebra 2, or is it something totally different?

Thanks a lot,

2. Jul 27, 2005

### quasar987

ummm. The idea of the Gaussian plane is to represent complex numbers as vectors. We chose the x-axis to host the real part of the complex number and the y-axis to host the imaginary part. Thus a complex number a+bi has the vector representation (a,b) in the Gaussian plane.

though you might not completely understand this, I will add that $\mathbb{C}$ and $\mathbb{R}^2$, as groups, are isomorphic to one another [according to the isomorphism that assigns to each complex number its corresponding vector in the Gaussian plane: f(a+bi) = (a,b)].
Maybe someone else can extrapolate on what intesresting things this implies; I'd be interested. Thx.

Last edited: Jul 27, 2005
3. Jul 27, 2005

### mathmike

a smooth translation from trig is non existent. calculus is just alot of algebra with a few more formulas thrown in. dont let it scare you though, it isnt as hard as you think

4. Jul 28, 2005

### HallsofIvy

Staff Emeritus
That's just a way of representing the complex numbers. Just as we can think of real numbers as numbers on a "number line", since every complex number, a+ bi, requires two real numbers, we need two number lines to represent complex number. It happens to be simplest to make those number lines perpendicular. The complex number a+bi is represented by the pair (a,b) in an obvious way and that corresponds to the point with coordinates (a, b).