# Worksheet: The Argument of a Complex Number

In this worksheet, we will practice identifying the argument of a complex number calculating it.

Q1:

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

• A
• B
• C1.3
• D
• E0.27

Q2:

Consider the complex number .

Find the argument of .

• A
• B
• C
• D
• E7

Hence, find the argument of .

• A
• B
• C
• D
• E

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?

• AIt is unchanged.
• BIt is increased by the argument of .
• CIt is increased by twice the argument of .
• DIt is increased by twice the argument of .
• EIt is increased by .

Q4:

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

• A0.64
• B0.67
• C0.89
• D0.93
• E0.54

Q5:

What is the argument of the complex number ?

• A
• B
• C
• D
• E

Q6:

What is the argument of the complex number , where ?

• A
• B
• C
• D
• E

Q7:

What is the argument of the complex number , where and ?

• A
• B
• C
• D
• E

Q8:

What does the argument of a complex number represent?

• Aits imaginary coordinate in the complex plane
• Bits real coordinate in the complex plane
• Cthe angle it makes with the positive real axis
• Dthe angle it makes with the positive imaginary axis
• Eits distance from the origin in the complex plane

Q9:

Given a complex number , where the principal argument of is , determine the principal argument of .

• A
• B
• C
• D

Q10:

What is the argument of the complex number ?

• A
• B
• C
• D
• E

Q11:

Given that and , determine the principal argument of .

• A
• B
• C
• D

Q12:

If is the principal argument of the complex number then what is the principal argument of ?

• A
• B
• C
• D

Q13:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q14:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q15:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q16:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q17:

Given that , find the principal argument of .

• A0
• B
• C
• D

Q18:

Given that , find the principal argument of .

• A
• B
• C
• D

Q19:

In what interval does the principal argument of a complex number lie?

• A
• B
• C
• D
• E

Q20:

What is the principal argument of the complex number , where and are real, which lies in the second quadrant of the Argand diagram?

• A
• B
• C
• D
• E

Q21:

Consider the complex number .