Lesson Worksheet: Introduction to Complex Numbers Mathematics

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:

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

  • AFalse
  • BTrue

Q2:

If 𝑧=5+2𝑖, what is Re(𝑧)?

Q3:

If 𝑧=46𝑖, what is Im(𝑧)?

Q4:

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

  • AFalse
  • BTrue

Q5:

What type of number is 3+5𝑖?

  • Areal
  • Bcomplex
  • Cpurely imaginary

Q6:

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

Q7:

What is the imaginary part of the complex number 22𝑖?

Q8:

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

Q9:

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

Q10:

If 𝑧=43𝑖, which of the following statements is correct?

  • ARe(𝑧)=3, Im(𝑧)=4
  • BRe(𝑧)=4, Im(𝑧)=3
  • CRe(𝑧)=3, Im(𝑧)=4
  • DRe(𝑧)=3, Im(𝑧)=4
  • ERe(𝑧)=4, Im(𝑧)=3

Q11:

Add 4 to 𝑖.

  • A4𝑖
  • B4+𝑖
  • C4𝑖
  • D4+𝑖
  • E4𝑖

Q12:

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

  • ATrue
  • BFalse

Q13:

Express 54 in terms of 𝑖.

  • A26𝑖
  • B36𝑖
  • C36
  • D36𝑖
  • E32𝑖

Q14:

The complex numbers are a field in part because .

  • A is a real vector space
  • Bfor every non-zero 𝑧 there is a 𝑤 such that 𝑧𝑤=1
  • C|𝑧|0 for all 𝑧
  • D

Q15:

Find the value of 144.

  • A12𝑖
  • B144𝑖
  • C12
  • D12
  • E12𝑖

Q16:

What is 25?

  • A25𝑖
  • B5𝑖
  • C5
  • D5𝑖
  • E5

Q17:

What type of number is 12𝑖?

  • AReal
  • BPure imaginary
  • CComplex

Q18:

Which of the following defines 𝑖?

  • AIt is the number whose square equals 1.
  • BIt is the number whose square equals 2.
  • CIt is the number whose square equals 1.
  • DIt is the number whose square equals 2.

Q19:

Solve the following equation: 𝑥+4=0.

  • A𝑥=+2,2
  • B𝑥=+4𝑖,4𝑖
  • C𝑥=4𝑖
  • D𝑥=2𝑖
  • E𝑥=+2𝑖,2𝑖

Q20:

True or False: The solution of the equation 𝑥+1=0 exists in the set of real numbers .

  • ATrue
  • BFalse

Q21:

What is the value of 𝑖?

Q22:

What is the value of 3𝑖?

Q23:

What is the value of 216?

  • A8
  • B8𝑖
  • C32𝑖
  • D32𝑖
  • E8

Q24:

Complete the following: If the two complex numbers 2+𝑥𝑖 and 𝑦+3𝑖 are equal, then 𝑥= and 𝑦=.

  • A3, 2
  • B3, 4
  • C2, 2
  • D2, 3
  • E3, 3

Q25:

Find 16.

  • A16𝑖
  • B4𝑖
  • C4
  • D4
  • E4𝑖

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