complex number qu (1 Viewer)

[lisarh]

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]

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]

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=)

 

[friction]

Beaten to it. Took me so long to write those 3 lines.

 

[lyounamu]

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

 

[lisarh]

Thanks guys.

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]