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

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- Thread starter Atilla1982
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Anyone got a good link to a place that explains complex numbers?

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arildno

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What do you want to know about them?

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

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Hurkyl

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arildno

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As Hurkyl said, just think of the good ole plane here.Atilla1982 said:I'm having a hard time rewriting from one form to another, carthesian - polar and so on.

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:

[tex]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}}})[/tex]

Find the angle [tex]\theta[/tex] that is the solution of the system of equations:

[tex]\frac{a} {\sqrt{a^{2}+b^{2}}}=\cos\theta,\frac{b}{\sqrt{a^{2}+b^{2}}}=\sin\theta[/tex]

Thus, defining [tex]|z|={\sqrt{a^{2}+b^{2}}}[/tex], we get:

[tex]z=|z|(\cos\theta+i\sin\theta)=|z|e^{i\theta}[/tex]

by definition of the complex exponential.

- #6

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

- #7

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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).

[tex]z=|z|(\cos\theta+i\sin\theta)=|z|e^{i\theta}[/tex]

- #8

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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

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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

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Best Regards,

Edwin

- #11

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Edwin said: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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