# Complex numbers

1. ### Atilla1982

18
Anyone got a good link to a place that explains complex numbers?

2. ### arildno

12,015
What do you want to know about them?

3. ### Atilla1982

18
I'm having a hard time rewriting from one form to another, carthesian - polar and so on.

4. ### Hurkyl

16,090
Staff Emeritus
Well, the procedure is essentially identical to converting between rectangular and polar coordinates on the good ol' real plane, so if that's where you're having trouble, you can pick up one of your old textbooks and review.

5. ### arildno

12,015
As Hurkyl said, just think of the good ole plane here.

Examples:
Suppose that a complex number z is given by:
z=a+ib
where a,b are real numbers, and i the imaginary unit.
Then, multiply z with 1 in the following manner:
$$z=\frac{\sqrt{a^{2}+b^{2}}}{\sqrt{a^{2}+b^{2}}}(a+ib)={\sqrt{a^{2}+b^{2}}}(\frac{a}{\sqrt{a^{2}+b^{2}}}+i\frac{b}{\sqrt{a^{2}+b^{2}}})$$
Find the angle $$\theta$$ that is the solution of the system of equations:
$$\frac{a} {\sqrt{a^{2}+b^{2}}}=\cos\theta,\frac{b}{\sqrt{a^{2}+b^{2}}}=\sin\theta$$
Thus, defining $$|z|={\sqrt{a^{2}+b^{2}}}$$, we get:
$$z=|z|(\cos\theta+i\sin\theta)=|z|e^{i\theta}$$
by definition of the complex exponential.

6. ### jaap de vries

254
buy a ti 89 or voyage 200 and your problems are forever solved

686
8. ### Edwin

167
Euler Identity

Here is a cool trick for calculating pi derived from Euler Identity.

e^(i*(pi/2)) = Cos(90) + i*Sin(90)

ln(e^(i*(pi/2)) = ln(Cos(90) +i*Sin(90))

i*(pi/2)*lne = ln(Cos(90) +i*Sin(90))

pi = (1/i)*(2)*ln(Cos(90) +i*Sin(90))

pi = (i^4/i)*(2)*ln(Cos(90) +i*Sin(90))

pi = (-i)*(2)*ln(Cos(90) +i*Sin(90))

pi = (-2i)*ln(Cos(90) +i*Sin(90))

pi = ln((Cos(90) +i*Sin(90))^(-2i))

pi = ln(1/(Cos(90) +i*Sin(90))^(2i))

Just a cool trick!

Best Regards,

Edwin G. Schasteen

9. ### philosophking

174
"buy a ti 89 or voyage 200 and your problems are forever solved"

if his problem is understanding how certain things work, then i think his problem would stay untouched if he bought one of these caluclators.

10. ### Edwin

167
I have a TI-83 plus and a TI Voyage 200, and I carry them both with me everywhere I go! They are truely amazing computation devices for those of us that are numerically challenged or just plain lazy.

Best Regards,

Edwin

254