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Worksheet: The Argument of a Complex Number
Q1:
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 .
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:
Given that principal argument , determine principal argument .
- A
- B
- C
- D
- E
Q4:
Given that principal argument of and principal argument of , determine the principal argument of .
- A
- B
- C
- D
Q5:
What is the argument of the complex number , where and ?
- A
- B
- C
- D
- E
Q6:
Given that the principal argument of and the principal argument of , determine the principal argument of .
- A
- B
- C
- D
- E
Q7:
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
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:
Find the argument of the complex number in radians. Give your answer correct to two decimal places.
- A
- B0.27
- C
- D
- E1.3
Q11:
What is the argument of the complex number , where ?
- A
- B
- C
- D
- E
Q12:
What is the argument of the complex number ?
- A
- B
- C
- D
- E