Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

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.

  • 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 ?

  • 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
  • B7
  • C
  • D
  • E

Hence, find the argument of .

  • A
  • B
  • C
  • D
  • E

Q8:

Find the modulus of the complex number .

  • A
  • B4
  • C
  • D1
  • E2

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 .

  • A2
  • B
  • C
  • D
  • E

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 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 .