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

Q1:

Find the argument of the complex number 2 β 7 π in radians. Give your answer correct to two decimal places.

Q2:

Consider the complex number π§ = 7 + 7 π .

Find the argument of π§ .

Hence, find the argument of π§ 4 .

Q3:

A complex number is multiplied by another complex number π§ , and then by the complex conjugate π§ β . How is the argument of the original complex number affected?

Q4:

Find the argument of the complex number 4 + 3 π in radians. Give your answer correct to two decimal places.

Q5:

What is the argument of the complex number 4 π ?

Q6:

What is the argument of the complex number π π , where π < 0 ?

Q7:

What is the argument of the complex number π + π π , where π > 0 and π > 0 ?

Q8:

Given that principal argument ( π ) = 5 π 6 , determine principal argument οΉ π ο 2 .

Q9:

Given that principal argument of π = 1 3 π 1 2 2 1 and principal argument of π = 3 π 4 2 2 , determine the principal argument of π π 4 1 2 2 .

Q10:

What does the argument of a complex number represent?

Q11:

Given a complex number π , where the principal argument of π is π = 1 1 π 1 2 , determine the principal argument of 1 0 π .

Q12:

Given that the principal argument of and the principal argument of , determine the principal argument of .

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