Lesson Plan: Loci in the Complex Plane Using the Modulus | Nagwa Lesson Plan: Loci in the Complex Plane Using the Modulus | Nagwa

# Lesson Plan: Loci in the Complex Plane Using the Modulus Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the loci of a complex equation in the complex plane from the modulus.

#### Objectives

Students will be able to

• describe loci of points constrained by conditions on their moduli geometrically,
• describe loci of points constrained by conditions on their moduli algebraically,
• apply the fact that the locus of a point that satisfies is a circle of radius ,
• apply the fact that the locus of a point that satisfies is the perpendicular bisector of the line segment joining and ,
• apply the fact that the locus of a point that satisfies , where , , is a circle,
• apply the fact that the locus of a point that satisfies , where , is an ellipse with foci and with a major axis of length .

#### Prerequisites

Students should already be familiar with

• complex numbers, in polar and Cartesian form,
• the complex plane.

#### Exclusions

Students will not cover

• transformations of the complex plane,
• Möbius transformations.

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