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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.

  • 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 .
  • Published