Find the locus in the complex plane of points that satisfy

In summary, the problem is asking to find the locus in the complex plane that satisfies z-c = p(1+it)/(1-it), where c is a complex number, p is a real number, and t is a real parameter. The solution involves a unit circle offset by c in the complex plane. However, it is important to note that the equation should be written as z-c = p(1+it)/(1-it) to avoid ambiguity.
  • #1
applestrudle
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Homework Statement



find the locus in the complex plane that satisfies

z -c = p (1+it/1-it)

c is complex, p is real t is a real parameter

Homework Equations





The Attempt at a Solution



there is no answer in the textbook so i wanted to check my answer. I got a unit circle which is offset by c, so that c is in the centre of the circle.

please confirm!
Thanks :)
 
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  • #2
are you sure it is a unit circle? remember 'p' is a real number there. Also, you should really put parentheses where they are needed. The equation should be written z-c = p (1+it)/(1-it) because this is unambiguous, however z-c = p(1+it/1-it) is very ambiguous and could mean a lot of different things.
 

FAQ: Find the locus in the complex plane of points that satisfy

What is a locus?

A locus is a set of points that satisfy a given condition or set of conditions. In other words, it is the path or curve traced out by a point that meets certain criteria.

What is the complex plane?

The complex plane, also known as the Argand plane, is a geometric representation of complex numbers. It is similar to the Cartesian coordinate system, with the horizontal axis representing the real numbers and the vertical axis representing the imaginary numbers.

How do you find the locus in the complex plane?

To find the locus in the complex plane, you must first identify the condition or set of conditions that the points must satisfy. Then, you can plot the points on the complex plane and observe the pattern or curve that is formed. This will give you the locus of the points.

What types of conditions can be used to find the locus in the complex plane?

The conditions used to find the locus in the complex plane can vary based on the specific problem. Some common conditions include equations, inequalities, and geometric properties such as distance or angle.

Why is finding the locus in the complex plane important?

Finding the locus in the complex plane can help solve various mathematical problems and equations. It also allows for a visual representation of complex numbers and their relationships, making it a useful tool in understanding and analyzing complex functions and equations.

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