In this worksheet, we will practice identifying the argument of a complex number and calculating it.

**Q2: **

Consider the complex number .

Find the argument of .

- A
- B
- C7
- D
- E

Hence, find the argument of .

- A
- B
- C
- D
- E

**Q3: **

A complex number is multiplied by another complex number , and then by the complex conjugate . How is the argument of the original complex number affected?

- AIt is increased by twice the argument of .
- BIt is increased by twice the argument of .
- CIt is increased by .
- DIt is unchanged.
- EIt is increased by the argument of .

**Q4: **

Find the argument of the complex number in radians. Give your answer correct to two decimal places.

- A0.67
- B 0.54
- C0.93
- D 0.64
- E0.89

**Q5: **

What is the argument of the complex number ?

- A
- B
- C
- D
- E

**Q6: **

What is the argument of the complex number , where ?

- A
- B
- C
- D
- E

**Q7: **

What is the argument of the complex number , where and ?

- A
- B
- C
- D
- E

**Q8: **

What does the argument of a complex number represent?

- A the angle it makes with the positive imaginary axis
- B its distance from the origin in the complex plane
- C its real coordinate in the complex plane
- D the angle it makes with the positive real axis
- E its imaginary coordinate in the complex plane

**Q9: **

Given a complex number , where the principal argument of is , determine the principal argument of .

- A
- B
- C
- D

**Q10: **

What is the argument of the complex number ?

- A
- B
- C
- D
- E

**Q11: **

Given that and , determine the principal argument of .

- A
- B
- C
- D

**Q12: **

If is the principal argument of the complex number then what is the principal argument of ?

- A
- B
- C
- D

**Q13: **

Given that , find the principal argument of rounded to the nearest two decimal places.

**Q14: **

Given that , find the principal argument of rounded to the nearest two decimal places.

**Q15: **

Given that , find the principal argument of rounded to the nearest two decimal places.

**Q16: **

Given that , find the principal argument of rounded to the nearest two decimal places.

**Q17: **

Given that , find the principal argument of .

- A
- B
- C0
- D

**Q18: **

Given that , find the principal argument of .

- A
- B
- C
- D

**Q19: **

In what interval does the principal argument of a complex number lie?

- A
- B
- C
- D
- E

**Q20: **

What is the principal argument of the complex number , where and are real, which lies in the second quadrant of the Argand diagram?

- A
- B
- C
- D
- E