# Worksheet: Modulus of a Complex Number

In this worksheet, we will practice using the general formula for calculating the modulus of a complex number.

**Q1: **

What is the modulus of the complex number ?

**Q2: **

What is the modulus of the complex number ?

- A3
- B10
- C
- D1
- E

**Q4: **

What is the modulus of the complex number ?

**Q7: **

Given that , find .

- A
- B
- C
- D
- E

**Q10: **

Given that , determine .

**Q12: **

If , where is a complex number, what is ?

**Q13: **

Given that , where and , write in algebraic form and hence find .

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

**Q14: **

Given that , where and , write in algebraic form and hence find .

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

**Q15: **

Given the complex number , what is the modulus of ?

- A
- B
- C
- D
- E

**Q17: **

Given that , where and are real numbers, determine the value of .

**Q18: **

Consider the complex numbers and . Given that and , which of the following is a possible value for ?

- A
- B
- C
- D
- E

**Q19: **

If and , what is ?

- A13
- B85
- C
- D145
- E

**Q20: **

What does the modulus of a complex number represent?

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

**Q21: **

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

- A6
- B
- C3
- D

**Q22: **

What is given that ?

- A36
- B100
- C
- D6
- E

**Q23: **

Consider the complex numbers and .

Find and .

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

Calculate . How does this compare with ?

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

Calculate . How does this compare with ?

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

**Q24: **

Consider the two complex numbers and .

Calculate to two decimal places.

Calculate to two decimal places.

Which of the following relations do and satisfy?

- A
- B
- C
- D
- E

**Q25: **

If , where is a complex number, what is ?