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