Question 1156361
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For any complex number {{{z = a+bi}}}, the magnitude of the complex number is {{{abs(z) = sqrt(a^2+b^2)}}}. 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 {{{abs(z) = 1}}}, so {{{sqrt(a^2+b^2) = 1}}} which becomes {{{a^2+b^2 = 1}}} when we square both sides. Note how (a,b) = (x,y), so we go from {{{a^2+b^2 = 1}}} to {{{x^2+y^2 = 1}}}


{{{x^2+y^2 = 1}}} is a circle with radius 1 and center (0,0). Compare this to the general form {{{(x-h)^2+(y-k)^2 = r^2}}}.


The diagram will be an empty (or not filled in) circle because we're only considering points on the circle itself. 


Similar problem:
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