# Complex numbers

by Atilla1982
Tags: complex, numbers
 P: 18 Anyone got a good link to a place that explains complex numbers?
 Sci Advisor HW Helper PF Gold P: 12,016 What do you want to know about them?
 P: 18 I'm having a hard time rewriting from one form to another, carthesian - polar and so on.
 Emeritus Sci Advisor PF Gold P: 16,091 Complex numbers 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.
HW Helper
PF Gold
P: 12,016
 Quote by Atilla1982 I'm having a hard time rewriting from one form to another, carthesian - polar and so on.
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.
 P: 254 buy a ti 89 or voyage 200 and your problems are forever solved
 P: 686 Maybe these websites will be a little help for you: http://mathworld.wolfram.com/ComplexNumber.html http://www.clarku.edu/~djoyce/complex/polar.html I can only give you one tip: (i) Get familiar with graphical interpretation of the sine and cosine in a circle. (ii) Really try to understand the formula by examining the drawing of a complex number (like in the link above). $$z=|z|(\cos\theta+i\sin\theta)=|z|e^{i\theta}$$
 P: 167 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
 P: 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.
 P: 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
 P: 254 [QUOTE=Edwin]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. Well said my friend. Understanding how it works does not mean that you need to bust your chops doing it the hard way all the time.

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