# Worksheet: Finding the Modulus of a Complex Number

Q1:

What is the modulus of the complex number ?

Q2:

Given that , find .

• A
• B
• C
• D3
• E

Q3:

What is the modulus of the complex number ?

• A
• B3
• C1
• D
• E10

Q4:

What is the modulus of the complex number ?

• A
• B3
• C7
• D
• E58

Q5:

What is the modulus of the complex number ?

Q6:

Given that , find .

• A
• B
• C
• D
• E

Q7:

Given that , find .

• A
• B
• C
• D
• E

Q8:

Given that , find .

• A
• B
• C
• D
• E

Q9:

Given that , determine .

• A
• B
• C
• D

Q10:

Consider the complex number .

Find the modulus of .

Find the argument of .

• A
• B
• C
• D
• E2

Hence, use the properties of multiplication of complex numbers in polar form to find the modulus and argument of .

• Amodulus = , argument=
• Bmodulus = , argument =
• Cmodulus = 8, argument =
• Dmodulus = 8, argument =
• Emodulus = , argument =

Hence, find the value of .

Q11:

If and , what is the modulus of ?

Q12:

Given that , find .

Q13:

Given that , determine .

Q14:

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

• A
• B
• C
• D
• E

Q15:

If , where is a complex number, what is ?

• A
• B0
• C2
• D1

Q16:

Is it true that for all ?

• Ayes
• Bno

Q17:

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

• A ,
• B ,
• C ,
• D ,

Q18:

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

• A ,
• B ,
• C ,
• D ,

Q19:

What is the magnitude of the product of and ?

• A
• B
• C
• D
• E