Lesson: The Argument of a Complex Number Mathematics

In this lesson, we will learn how to identify the argument of a complex number and how to calculate it.

Lesson Plan

Objectives

Students will be able to

understand that the argument of a complex number, , is the angle that the line from the origin to makes with the positive real axis,
understand that the argument of a complex number is measured in a counterclockwise direction,
understand that the principle argument is usually given in radians in the range ,
find the argument of a complex number in any of the 4 quadrants using formulas involving arctan,
understand how to use the properties of the argument of a complex number (or its conjugate) to solve problems.

Prerequisites

Students should already be familiar with

complex numbers in Cartesian form,
the conjugate of a complex number,
operations on complex numbers in Algebraic (rectangular or Cartesian) form,
Argand diagrams.

Exclusions

Students will not cover

complex numbers in exponential form,
complex numbers in polar form.

Lesson Video

Lesson Explainer

Sample Question Videos

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04:47
04:05

Lesson Worksheet

Q1:

Find the argument of the complex number in radians. Give your answer correct to two decimal places.

Q2:

Consider the complex number .

Find the argument of .

Hence, find the argument of .

Q3:

A complex number is multiplied by another complex number , and then by the complex conjugate . How is the argument of the resulting complex number related to the argument of the original complex number?