# Worksheet: Polar Form of Complex Numbers

In this worksheet, we will practice representing a complex number in polar form, calculating the modulus and argument, and using this to change the form of a complex number.

Q1:

Find the trigonometric form of the complex number represented by the given Argand diagram. • A
• B
• C
• D

Q2:

Express in algebraic form.

• A
• B
• C
• D

Q3:

Find the modulus of the complex number .

• A1
• B
• C2
• D
• E4

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

Q4:

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

Q5:

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

Q6:

Express the complex number in trigonometric form.

• A
• B
• C
• D

Q7:

Given that , determine the trigonometric form of .

• A
• B
• C
• D
• E

Q8:

• A,
• B,
• C,
• D,

Q9:

• A,
• B,
• C,
• D,

Q10:

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

• A
• B
• C
• D

Q11:

Given that , express the complex number in the form of , and then determine its trigonometric form.

• A,
• B,
• C,
• D,

Q12:

• A,
• B,
• C,
• D,

Q13:

Given that and the argument of is , find , giving your answer in trigonometric form.

• A
• B
• C
• D
• E

Q14:

Given that and the argument of is , find , giving your answer in trigonometric form.

• A
• B
• C
• D
• E

Q15:

Given that and the argument of is , where , find , giving your answer in trigonometric form.

• A
• B
• C
• D
• E

Q16:

Given that and the argument of is , find , giving your answer in algebraic form.

• A
• B
• C
• D
• E

Q17:

Given that and the argument of is , find , giving your answer in algebraic form.

• A
• B
• C
• D
• E

Q18:

Given that and the argument of is , find , giving your answer in algebraic form.

• A
• B
• C
• D
• E

Q19:

Given that , determine the algebraic form of , approximating the real and imaginary parts to the nearest two decimal places.

• A
• B
• C
• D

Q20:

Given that , find the principal argument of , where .

• A
• B
• C
• D
• E

Q21:

Find .

• A
• B
• C
• D
• E

Find .

• A
• B
• C
• D
• E

Hence, express the complex number in rectangular form.

• A
• B
• C
• D
• E

Q22:

Given that , find .

Q23:

Find the modulus and the principal amplitude of the number .

• A, principal amplitude
• B, principal amplitude
• C, principal amplitude
• D, principal amplitude

Q24:

Find the modulus and the principal amplitude of the number .

• A, principal amplitude
• B, principal amplitude
• C, principal amplitude
• D, principal amplitude

Q25:

Find the modulus and the principal amplitude of the number .

• A, principal amplitude
• B, principal amplitude
• C, principal amplitude
• D, principal amplitude