Mapping a complex circle to its square

• torquerotates
In summary, to graph |z-1|=1 and z^2, we can first rewrite |z-1|=1 as (x-1)^2+y^2=1, which represents a circle. To incorporate z^2 into the graph, we can plot the set {(z, z^2): |z - 1| = 1}. However, it is recommended to seek clarification from the professor for further guidance.
torquerotates

Homework Statement

graph |z-1|=1 and then graph z^2

z=x+iy

The Attempt at a Solution

well, |z-1|=1 => |(x-1)+iy|=1,

squaring both sides. we get, (x-1)^2+y^2=1. This is a circle. But how am i supposed to get z^2 from this? I don't know what to do with the inequality since i can't algebrically isolate the z.

I'm confused, too. Maybe you're supposed to take the z values on the circle and square them. If that's the case, what you'd be graphing is the set {(z, z^2): |z - 1| = 1}.

If I were you, I'd get clarification from my prof.

1. How do you map a complex circle to its square?

Mapping a complex circle to its square involves using a mathematical formula or algorithm to transform the coordinates of points on the circle to coordinates on the square.

2. Why would you want to map a complex circle to its square?

Mapping a complex circle to its square can be useful in various applications such as computer graphics, image processing, and data visualization. It allows for easier manipulation and analysis of complex circular data.

3. What is the process for mapping a complex circle to its square?

The process involves translating the center of the circle to the center of the square, scaling the radius of the circle to match the side length of the square, and then using a mathematical formula or algorithm to map each point on the circle to a point on the square.

4. Are there different methods for mapping a complex circle to its square?

Yes, there are various methods for mapping a complex circle to its square, including the conformal mapping method, the stereographic projection method, and the trigonometric mapping method. Each method has its own advantages and limitations.

5. Is mapping a complex circle to its square a reversible process?

No, mapping a complex circle to its square is not a reversible process. While it is possible to map a circle to a square, it is not possible to map a square back to a circle using the same method. This is due to the fact that the square has four distinct corners while the circle has no corners.

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