More complex numbers~~ (1 Viewer)

[SeDaTeD]

I think this method can be applied in general to find nearest/furthest points on any continuous and differentiable curves from the origin. Take note that you may get more than 2 solutions, but you should be able to easily identify whihc ones are closest/furthest. It's like having a bubble that grows from the origin and the closest point is where it first touches the curve.

Mind you I don't think you'd need any of this for 4unit.

 

[Riviet]

For implicit differentiation, if you differentiate anything with y, use the chain rule
so for example: d/dx[y²]=2y[dy/dx)

 

[pLuvia]

For implicit you just differentiate the y then multiply dy/dx to it i.e.

y = x²y²
y' = x²2y[dy/dx] + 2xy²

 

[chochibi]

the 2nd part is easier to see if you draw a diagram..
basically if you tan both sides you get gradients.

arg (z-2-2i) = pi/3
tan(arg(y-2/x-2)) = -root3
y-2/x-2=-root3
y-2=-root3x+2root3
y=-root3x+2(1+root3)

dang.. this is hard to type.. i so prefer writing in 4u than typing..
anyways.. ther's a 50/50 chance that im wrong soo.. ye.. if it is then give me a holla.. cuz i wanna see what the right answer is..