Recent content by amr21

I don't think I understand, could you explain further? :)

Show geometrically that if |z|=1 then, $Im[z/(z+1)^2]=0$ I am unsure how to begin this problem. I have sketched out |z|=1 but can't work out how to sketch the Imaginary part of the question.

That makes sense, thank you! Could you explain further on how to find an x to match them?

Is it a circle with centre (-8,0) and a radius of 2?

Is the set of points for part (b) $\{w \in \mathbb C : |(w/2)+4|=1\}$ ? Could you explain how to plot the w/2 part? part (c) I believe the set is $\{w \in \mathbb C : |(-w/2)+4|=1\}$. Once again could you explain the -w/2 part part (d) do you flip the circle over the x-axis? part (e) I'm...

Is it the same circle reflected over the y-axis, so the mid-point is (4,0)?

Starting from the origin, go one unit east, then the same distance north, then (1/2) of the previous distance west, then (1/3) of the previous distance south, then (1/4) of the previous distance east, and so on. What point does this 'spiral' converge to? I have attempted to sketch this out but...

I have a circle with centre (-4,0) and radius 1. I need to draw the image of this object under the following mappings: a) w=e^(ipi)z b) w = 2z c) w = 2e^(ipi)z d) w = z + 2 + 2i I have managed to complete the question for a square and a rectangle as the points are easy to map as they are...

Hello, I am struggling to understand a simple question on limits. I have watched a video trying to explain the theory and even have the answer right in front of me but I still don't understand. Could somebody please explain the steps in detail for me just for the first question as I'm hoping...