Question: Drawing of complex numbers on a complex "grid"

Hello everybody! Happy new year! 

Im back this year. I bought a flatbedscanner to scan some books. Already scanned 3 whole books in 2 days, its a blast!

Ive got a question about some complex numbers that i have to draw on a grid. 

The translated question is: "draw in the complex grid the following collections:"

Here is what ive got. But the book does not give any solutions for me to check on. So its not great at all to have to learn like that. 



-2+I = 2

sqrt((x-2)^2+(y+1)^2) = sqrt(2)

((x-2)^2+(y+1)^2)^(1/2) = 2^(1/2)


smartplot(sqrt((x-2)^2+(y+1)^2) = sqrt(2), sqrt((x-2)^2+(y+1)^2) = 1)






(1/2)*sqrt((x-4)^2+(y+2)^2) = 0

(1/2)*((x-4)^2+(y+2)^2)^(1/2) = 0


smartplot(sqrt((x-1)^2+(y+2)^2) = sqrt(3))



Error, `;` unexpected







sqrt(x^2+y^2) = 1

(x^2+y^2)^(1/2) = 1


sqrt(x^2+y^2) = 3

(x^2+y^2)^(1/2) = 3


smartplot(sqrt(x^2+y^2) = 1, sqrt(x^2+y^2) = 3, x = -(1/4)*Pi, x = 3*Pi*(1/4))















everything under y=0 and everything to the right of x=0

plot(x = 0 .. 10, y = -10 .. 0)



sqrt(x^2+y^2) = 0

(x^2+y^2)^(1/2) = 0


sqrt(x^2+y^2) = 2

(x^2+y^2)^(1/2) = 2


smartplot(sqrt(x^2+y^2) = 0, sqrt(x^2+y^2) = 2, x = -(1/4)*Pi, x = (1/3)*Pi)









The book gave an example, the translations says:"Draw in the complex grid the collection:

This we can read as: draw all complex numbers for which the distance to i is similar to 2. This collection is a circle in the complex grid with the center (0,1) and a radius of 2. See the figure on the left.

Draw in the complex grid the collection:


We can wright     This we can read as: Draw all complex numbers for which the distance to -3+2i is simular to 1. This collection is a circle in the complex grid, see the figure on the right. Another method is z=x+iy, we can substitute this into. This substitution delivers a relation between x and y, after which we can draw each z=x+iy that complies with |z+3-2i|=1. The substitution gives us:  frown which leads,   so that  . This is again a formula of a circle in the complex grid with the middlepoint (-3,2) and a radius of 1." 

Some more examples:

I also added a PDF of the chapter, so you can see what a flatbed scanner can do (a canon lide 400) and adobe DC (to combine the scans and perform "OCR" on the text so the computer can read the text so you can copy and paste it and search the text with CTRL+F. A must have if you are serious in doing studies in my opinion, its way way faster to look up things like that than to go to a register or glossary at the back of the book that may not even have the topic listed what you are looking for.). It is very impotant that you get good scans of the PDF program will not read your numbers and letters in the scanned file well. The solutions (after having scanned half a book already, so i had to do that part again) was to lay the book on the right side of the scanner, with half the book on top of the scanner. Press on the back of the book, and lay 2 hands on top to press the page (lightly) against the glass. When you are dont with that page, you invert the book and keep half the book on the right side again. The PDF program (adobe DC) will flip the scans for you with the OCR recognition function. 

I thought id share this with you, while this costed me 2 books to find this out, and costed me a lot of time. Time a valuable, that is why i started the scanning in the first place. It better be good on the first run.  

Looking at the google translate results the "grid" probably is a "plane" just as in a 3d drawing program. 

Any way, i hope i was specific enough. Im having a bit of trouble with this planing of complex numbers. 


The Function. 



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