# 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

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:

• A,
• B,
• C,
• D,

Q12:

• A,
• B,
• C,
• D,

Q13: