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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