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For any complex number , the magnitude of the complex number is . We can see this through finding the distance from (0,0) to (a,b). This is effectively the same as using the pythagorean theorem.
We want , so which becomes when we square both sides. Note how (a,b) = (x,y), so we go from to
is a circle with radius 1 and center (0,0). Compare this to the general form .
The diagram will be an empty (or not filled in) circle because we're only considering points on the circle itself.
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