Complex Circles: Path of |z-i| = pi

In summary, the equation for "Complex Circles: Path of |z-i| = pi" is |z-i| = pi. The absolute value in this equation represents the distance of the complex number z from the point i on the complex plane. There are infinitely many solutions for this equation as it represents a circle with a radius of pi centered at the point i on the complex plane. The value of pi determines the radius of the circle, so a larger value of pi will result in a larger circle while a smaller value of pi will result in a smaller circle. This equation cannot be graphed on a Cartesian plane as it involves complex numbers which require a separate complex plane to graph.
  • #1
ultramat
1
0

Homework Statement



I'm not sure how the graph looks like for the path |z-i| = pi

Homework Equations



I know that if the function is |z-i|=1 means a unit circle center at i


The Attempt at a Solution



Does that mean |z-i|=pi is a circle center at pi with a radius of pi?

Thanks
 
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  • #2
No. Remember that |a- b| is the distance from a to b in the complex plane. |z- i| says that the distance from the variable point z to the point i is pi. Yes, that's a circle. What is its center?
 

1. What is the equation for "Complex Circles: Path of |z-i| = pi"?

The equation for "Complex Circles: Path of |z-i| = pi" is |z-i| = pi.

2. What is the meaning of the absolute value in this equation?

The absolute value in this equation represents the distance of the complex number z from the point i on the complex plane.

3. How many solutions are there for this equation?

There are infinitely many solutions for this equation as it represents a circle with a radius of pi centered at the point i on the complex plane.

4. How does the value of pi affect the shape of the circle?

The value of pi determines the radius of the circle, so a larger value of pi will result in a larger circle while a smaller value of pi will result in a smaller circle.

5. Can this equation be graphed on a Cartesian plane?

No, this equation cannot be graphed on a Cartesian plane as it involves complex numbers which require a separate complex plane to graph.

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