# Worksheet: The Argument of a Complex Number

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

**Q3: **

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

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

**Q4: **

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

**Q8: **

What does the argument of a complex number represent?

- Aits imaginary coordinate in the complex plane
- Bits real coordinate in the complex plane
- Cthe angle it makes with the positive real axis
- Dthe angle it makes with the positive imaginary axis
- Eits distance from the origin in the complex plane

**Q9: **

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

**Q16: **

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

**Q17: **

Given that , find the principal argument of .

- A0
- B
- C
- 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

**Q21: **

Consider the complex number .

Calculate , giving your answer correct to two decimal places in an interval from to .

Calculate , giving your answer correct to two decimal places in an interval from to .

**Q22: **

Consider the complex numbers and .

Find and .

- A,
- B,
- C,
- D,
- E,

Calculate . How does this compare to and ?

- A,
- B,
- C,
- D,
- E,

Calculate . How does this compare to and ?

- A,
- B,
- C,
- D,
- E,

**Q23: **

If is the principal argument of a complex number , determine the argument of .

- A
- B
- C
- D

**Q24: **

Given that principal argument , determine principal argument .

- A
- B
- C
- D
- E

**Q25: **

Given that principal argument of and principal argument of , determine the principal argument of .

- A
- B
- C
- D