Lesson: Loci in the Complex Plane Using the Modulus Mathematics
In this lesson, we will learn how to find the loci of a complex equation in the complex plane from the modulus.
A complex number satisfies .
Describe the locus of and give its Cartesian equation.
What is the minimum value of ?
The figure shows a locus of point in the complex plane, which is an ellipse with foci and and major axis . represents the number , the number , the number , and the number . Using the properties of an ellipse, write an equation for the locus of point in terms of .
A complex number satisfies . Find the Cartesian equation of the locus of and describe it geometrically.