complex number qu (1 Viewer)

lisarh

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The complex number z=x+iy, x and y real, is such that

| z-i | = Im (z)

Find the locus of the point representing z.


Answer is y=1/2.(x^2+1)
 

munch0r

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LHS = | x + yi - i |
RHS = y
Therefore | x + i(y-1) | = y
sqrt(x^2 + (y-1)^2) = | x + i(y-1) |
x^2 + (y-1)^2 = y^2
2y = x^2 + 1
y = 1/2 . (x^2 + 1)
 

friction

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

x^2 + y ^ 2 - 2y + 1 = y^2

y = 1/2 ( x^2 +1) (by rearranging so y=)
 

lyounamu

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So many people accelerate on their own...I feel so behind...
 

lisarh

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Thanks guys.


lyounamu said:
So many people accelerate on their own...I feel so behind...
What, are you kidding me? Lyounamu, you are like the smartest guy I know of around here. I bet ya you can easily do these questions if you know how to. Unlike me, I struggle. x]
 

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