# Worksheet: Finding the Argument of a Complex Number

Q1:

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

• A
• B0.27
• C
• D
• E1.3

Q2:

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

• A0.67
• B 0.54
• C0.93
• D 0.64
• E0.89

Q3:

What is the argument of the complex number ?

• A
• B
• C
• D
• E

Q4:

What is the argument of the complex number ?

• A
• B
• C
• D
• E

Q5:

What is the argument of the complex number , where ?

• A
• B
• C
• D
• E

Q6:

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

• A
• B
• C
• D
• E

Q7:

Consider the complex number .

Find the argument of .

• A
• B
• C7
• D
• E

Hence, find the argument of .

• A
• B
• C
• D
• E

Q8:

Find the modulus of the complex number .

• A1
• B2
• C4
• D
• E

Find the argument of the complex number .

• A
• B
• C
• D
• E

Hence, write the complex number in polar form.

• A
• B
• C
• D
• E

Q9:

Consider the complex number .

Find the modulus of .

Find the argument of .

• A
• B
• C
• D
• E2

Hence, use the properties of multiplication of complex numbers in polar form to find the modulus and argument of .

• Amodulus = , argument=
• Bmodulus = , argument =
• Cmodulus = 8, argument =
• Dmodulus = 8, argument =
• Emodulus = , argument =

Hence, find the value of .

Q10:

What is the argument of the product of and ?

• A
• B
• C
• D
• E

Q11:

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

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