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Worksheet: Introduction to Complex Numbers

Q1:

If 𝑧 = 5 + 2 𝑖 , what is 𝑅 𝑒 ( 𝑧 ) ?

Q2:

What is the value of 𝑖 2 ?

Q3:

The complex numbers β„‚ are a field in part because .

  • A β„‚ is a real vector space
  • B ℝ βŠ‚ β„‚
  • C | 𝑧 | β‰₯ 0 for all 𝑧 ∈ β„‚
  • Dfor every non-zero 𝑧 ∈ β„‚ there is a 𝑀 ∈ β„‚ such that 𝑧 𝑀 = 1

Q4:

What is the value of 3 𝑖 2 ?

Q5:

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

Q6:

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.

Q7:

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

  • ATrue
  • BFalse

Q8:

Simplify 1 𝑖 .

  • A1
  • B 𝑖
  • C βˆ’ 1
  • D βˆ’ 𝑖

Q9:

What type of number is βˆ’ 3 + 5 𝑖 ?

  • Apurely imaginary
  • Breal
  • Ccomplex

Q10:

Add 4 to βˆ’ 𝑖 .

  • A βˆ’ 4 βˆ’ 𝑖
  • B 4 + 𝑖
  • C βˆ’ 4 + 𝑖
  • D 4 βˆ’ 𝑖
  • E βˆ’ 4 𝑖

Q11:

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

Q12:

If 𝑧 = 4 βˆ’ 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 ) = βˆ’ 3 , I m ( 𝑧 ) = 4
  • D R e ( 𝑧 ) = 4 , I m ( 𝑧 ) = βˆ’ 3
  • E R e ( 𝑧 ) = βˆ’ 3 , I m ( 𝑧 ) = βˆ’ 4

Q13:

What is the imaginary part of the complex number 2 βˆ’ 2 𝑖 ?

Q14:

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

  • Afalse
  • Btrue

Q15:

If 4 + π‘š 𝑖 is a real number, what is the value of π‘š ?

Q16:

What is the value of 𝑖 7 ?

  • A 𝑖
  • B βˆ’ 1
  • C1
  • D βˆ’ 𝑖

Q17:

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

  • Atrue
  • Bfalse

Q18:

If 𝑧 = βˆ’ 4 βˆ’ 6 𝑖 , what is 𝐼 π‘š ( 𝑧 ) ?