Worksheet: Finding the Argument of a Complex Number

Cement your understanding of what the argument of a complex number is and how to calculate it in this worksheet. Practice calculating the argument in a series of problems and then using this argument to rewrite complex numbers.

Q1:

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

A1.3
B
C
D
E0.27

Q2:

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

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

Q3:

What is the argument of the complex number ?

Q4:

What is the argument of the complex number ?

Q5:

What is the argument of the complex number , where ?

Q6:

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

Q7:

Consider the complex number .

Find the argument of .

Hence, find the argument of .

Q8:

Find the modulus of the complex number .

Find the argument of the complex number .

Hence, write the complex number in polar form.

Q9:

Consider the complex number .

Find the modulus of .

Find the argument of .

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 ?

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