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Worksheet: Representing Complex Numbers in Polar Form

Q1:

What do we need to do to multiply two complex numbers in polar form?

  • Aadd their moduli together and multiply their arguments
  • Badd their moduli together and add their arguments
  • Cmultiply their moduli together and multiply their arguments
  • Dmultiply their moduli together and add their arguments
  • Emultiply their moduli together and subtract their arguments

Q2:

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

Q3:

Consider the diagram.

Which of the following correctly describes the relationship between and ?

  • A
  • B
  • C
  • D
  • E

Which of the following correctly describes the relationship between and ?

  • A
  • B
  • C
  • D
  • E

Hence, express in terms of and .

  • A
  • B
  • C
  • D
  • E

Q4:

Find the trigonometric form of the complex number represented by the given Argand diagram.

  • A
  • B
  • C
  • D

Q5:

Find the trigonometric form of the complex number represented by the given Argand diagram.

  • A
  • B
  • C
  • D

Q6:

The Argand diagram shows the complex number .

Write in rectangular form.

  • A
  • B
  • C
  • D
  • E

Convert to polar form, rounding the argument to two decimal places.

  • A
  • B
  • C
  • D
  • E

Q7:

Express the complex number in trigonometric form.

  • A
  • B
  • C
  • D

Q8:

Given that , determine the trigonometric form of .

  • A
  • B
  • C
  • D
  • E

Q9:

Given that , determine the trigonometric form of .

  • A
  • B
  • C
  • D
  • E

Q10:

If , what is ?

  • A
  • B
  • C
  • D

Q11:

Simplify , giving your answer in both algebraic and trigonometric form.

  • A ,
  • B ,
  • C ,
  • D ,

Q12:

Simplify , giving your answer in both algebraic and trigonometric form.

  • A ,
  • B ,
  • C ,
  • D ,

Q13:

Simplify , giving your answer in both algebraic and trigonometric form.

  • A ,
  • B ,
  • C ,
  • D ,

Q14:

Given that , determine the trigonometric form of the complex number .

  • A