Worksheet: Introduction to Complex Numbers

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In this worksheet, we will practice dealing with imaginary numbers, knowing that complex numbers are made of a real part and an imaginary part.

Q1:

Is the following statement true or false: Any complex number is also a real number.

  • Afalse
  • Btrue

Q2:

If 𝑧 = 5 + 2 𝑖 , what is 𝑅 𝑒 ( 𝑧 ) ?

Q3:

If 𝑧 = − 4 − 6 𝑖 , what is 𝐼 𝑚 ( 𝑧 ) ?

Q4:

Which of the following statements will be true of two equal complex numbers?

  • ATheir real parts will not be equal and their imaginary parts will be equal.
  • BTheir real parts will be equal and their imaginary parts will not be equal.
  • CTheir real parts will not be equal and their imaginary parts will not be equal.
  • DTheir real parts will be equal and their imaginary parts will be equal.

Q5:

Is the following statement true or false: Any imaginary number is also a complex number.

  • Atrue
  • Bfalse

Q6:

What type of number is − 3 + 5 𝑖 ?

  • Apurely imaginary
  • Breal
  • Ccomplex

Q7:

What is the real part of the complex number 3 + 4 𝑖 ?

Q8:

What is the imaginary part of the complex number 2 − 2 𝑖 ?

Q9:

If 4 + 𝑚 𝑖 is a real number, what is the value of 𝑚 ?

Q10:

If 𝑝 + 2 𝑖 is an imaginary number, what is the value of 𝑝 ?

Q11:

If 𝑧 = 4 − 3 𝑖 , which of the following statements is correct?

  • A R e ( 𝑧 ) = 3 , I m ( 𝑧 ) = 4
  • B R e ( 𝑧 ) = 4 , I m ( 𝑧 ) = 3
  • C R e ( 𝑧 ) = − 3 , I m ( 𝑧 ) = 4
  • D R e ( 𝑧 ) = 4 , I m ( 𝑧 ) = − 3
  • E R e ( 𝑧 ) = − 3 , I m ( 𝑧 ) = − 4

Q12:

Add 4 to − 𝑖 .

  • A − 4 − 𝑖
  • B 4 + 𝑖
  • C − 4 + 𝑖
  • D 4 − 𝑖
  • E − 4 𝑖

Q13:

True or False: Any real number is also a complex number.

  • ATrue
  • BFalse

Q14:

Factor 𝑥 + 𝑦 2 2 over the complex numbers.

  • A ( 𝑥 + 𝑦 𝑖 ) ( 𝑥 + 𝑦 𝑖 )
  • B ( 𝑥 + 𝑦 ) ( 𝑥 − 𝑦 )
  • C ( 𝑥 − 𝑦 𝑖 ) ( 𝑥 − 𝑦 𝑖 )
  • D ( 𝑥 + 𝑦 𝑖 ) ( 𝑥 − 𝑦 𝑖 )
  • E ( 𝑥 + 𝑦 ) ( 𝑥 + 𝑦 )

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