Best Graph Software for Coursework - Find Complex Roots with Ease

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PlasmaSphere
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Hi ppl

Its not actually a maths question, as such, more a maths related question. I need to draw some basic graphs for my coursework, but i don't know what softwear to use. I need to use it to input simple functions and copy pictures of the graph onto my coursework, which is about Newton Raphson method and how to find complex roots.

At my school I use autograph v3, but it doesn't work on my home computer. I'm sure there must be a decent freeware graph program to play around with online, but i can't seem to find one. Any softwear reccomendations would be appreciated, thanx
 
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Probably a little old fashioned in the Vista/Leopard era but I always liked gnuplot.
 
GrafEq is amazing at graphing complicated implicit or explicit functions, and has many, many trigonometric functions, gamma function, etc... built in. Play around with it a bit, and you'll be a pro. ftp://ftp.peda.com/grafeq32.exe
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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