**Q1: **

Consider the complex number .

Find the modulus of .

- A1
- B3
- C
- D
- E

Hence, find the modulus of .

- A
- B10
- C
- D243
- E

**Q2: **

Find the complex number such that lies at the midpoint of and when they are represented on a complex plane.

- A
- B
- C
- D
- E

**Q3: **

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

**Q4: **

Find the possible real values of such that the distance between the complex number and the complex number is 5.

- A 5 or 9
- B 5
- C 1.7 or 15.7
- D 3 or 11
- E 0.5 or 14.5

**Q5: **

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

**Q6: **

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

**Q7: **

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

**Q8: **

Given that , find the principal argument of .

- A
- B
- C0
- D

**Q9: **

Given that , find the principal argument of .

- A
- B
- C
- D

**Q10: **

Let us consider a complex number, , with nonzero real and imaginary parts.

If the real and imaginary parts of are of the same sign, in which quadrant(s) of the Argand diagram could appear?

- A1st or 2nd
- B2nd or 4th
- C3rd or 4th
- D1st or 3rd
- E1st or 4th

If the real and imaginary parts of are of opposite signs, in which quadrant(s) of the Argand diagram could appear?

- A2nd or 4th
- B3rd or 4th
- C1st or 2nd
- D1st or 3rd
- E1st or 4th

**Q11: **

What complex number lies at the midpoint of the complex numbers and , where , , , and are real, when they are represented on a complex plane?

- A
- B
- C
- D
- E

**Q12: **

Given that , determine the real part of the complex number .

- A6
- B3
- C
- D

**Q13: **

What does the modulus of a complex number represent?

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

**Q14: **

Simplify , giving your answer in algebraic form.

- A
- B
- C
- D

**Q15: **

If , find .

- A
- B
- C
- D
- E