# 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 ?

- A10
- B3
- C
- D1
- E

**Q3: **

What is the modulus of the complex number ?

- A7
- B3
- C
- D
- E58

**Q4: **

What is the modulus of the complex number ?

**Q6: **

Given that , find .

- A3
- B
- C
- D
- E

**Q7: **

Given that , find .

- A
- B
- C
- D
- E

**Q8: **

Given that , determine .

- A
- B
- C
- D

**Q9: **

If and , what is the modulus of ?

**Q10: **

Given that , determine .

**Q11: **

What is the modulus of the complex number , where and are real?

- A
- B
- C
- D
- E

**Q12: **

If , where is a complex number, what is ?

- A0
- B2
- C
- D1

**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 .

- A
- B
- C 29
- D

**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 ?

- A85
- B13
- C145
- D
- E

**Q20: **

What does the modulus of a complex number represent?

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

**Q21: **

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

- A
- B
- C6
- D3

**Q22: **

What is given that ?

- A
- B
- C100
- D36
- E6

**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