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Worksheet: Polar Form of a Complex Number

Q1:

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

  • Amultiply their moduli together and subtract their arguments
  • Bmultiply their moduli together and multiply their arguments
  • Cmultiply their moduli together and add their arguments
  • Dadd their moduli together and multiply their arguments
  • Eadd their moduli together and add their arguments

Q2:

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

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
  • B