Worksheet: Polar Form of Complex Numbers

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:

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

A,
B,
C,
D,

Q9:

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

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:

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

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