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#1 2019-10-14 19:29:02
- 666 bro
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- From: Flatland
- Registered: 2019-04-26
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Using limits with complex numbers
Hi guys,
Now I'm learning limits and derivatives
My question is how can I apply graphical limits in an argands plane?
"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan
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#2 2019-10-14 19:42:03
- Bob
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- Registered: 2010-06-20
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Re: Using limits with complex numbers
hi 666 bro
Sorry, I'm not following exactly what you are asking. Please give more details.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2019-10-14 21:12:43
- 666 bro
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- From: Flatland
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Re: Using limits with complex numbers
In an argands plane how could we apply limits to them and how ''z'' could be the considered as a function of the graph?
Last edited by 666 bro (2019-10-14 21:40:29)
"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan
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#4 2019-10-15 00:45:30
- Bob
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Re: Using limits with complex numbers
hi 666 bro
Strictly speaking, the Argand diagram is not a graph. As it has 'x' and 'y' coordinates I can see why you might think it was. But it is just a way to represent complex numbers and there is lots of useful maths that stems from it.
A function such as y = 2x + 3 has an input (x) and an output (y). So you can show the effect of the function by plotting a graph.
A function like z = x^2 + y^2 cannot be represented in 2 dimensions, so, if you want a visual representation you have to try and represent the z axis, perpendicular to the other two … usually rising up from the x-y plane. Tricky to show clearly because we are only 3 dimensional beings (as far as I can tell )
So if that was the function of complex numbers of the form x + iy and z was limited to real values that's how you'd have to graph it. But z could also be complex in which case we run out of dimensions to show what is happening. Nevertheless there's a whole area of maths that does consider such functions.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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