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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