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Homework Help

Lesson: Dividing Complex Numbers

In this lesson, we will learn how to perform division on complex numbers.

Sample Question Videos

03:20
02:10

Worksheet • 14 Questions • 2 Videos

Q1:

Simplify βˆ’ 1 2 βˆ’ 4 𝑖 2 𝑖 .

  • A βˆ’ 2 + 6 𝑖
  • B 8 βˆ’ 2 4 𝑖
  • C 2 + 2 4 𝑖
  • D βˆ’ 4 + 1 2 𝑖

Q2:

Simplify 2 3 + 𝑖 .

  • A ( 3 βˆ’ 𝑖 ) 5
  • B 2 3 + 2 𝑖
  • C 2 3 βˆ’ 2 𝑖
  • D 3 βˆ’ 𝑖
  • E ( 3 βˆ’ 𝑖 ) 1 0

Q3:

Put 2 βˆ’ 5 + 5 𝑖 in the form π‘Ž + 𝑏 𝑖 .

  • A βˆ’ 0 . 2 βˆ’ 0 . 2 𝑖
  • B βˆ’ 0 . 2 + 0 . 2 𝑖
  • C 0 . 2 βˆ’ 0 . 2 𝑖
  • D 0 . 2 + 0 . 2 𝑖

Q4:

Put βˆ’ 1 8 βˆ’ 9 𝑖 3 𝑖 in the form π‘Ž + 𝑏 𝑖 .

  • A βˆ’ 3 + 6 𝑖
  • B 2 7 βˆ’ 5 4 𝑖
  • C 3 + 5 4 𝑖
  • D βˆ’ 9 + 1 8 𝑖

Q5:

Simplify 1 3 1 3 + 2 𝑖 .

  • A 1 6 9 1 7 3 βˆ’ 2 6 1 7 3 𝑖
  • B 1 6 9 1 7 3 + 2 6 1 7 3 𝑖
  • C 1 6 9 1 6 5 + 2 6 1 6 5 𝑖
  • D 1 6 9 1 6 5 βˆ’ 2 6 1 6 5 𝑖

Q6:

Simplify 3 βˆ’ 6 𝑖 1 βˆ’ 5 𝑖 .

  • A 3 3 2 6 + 9 2 6 𝑖
  • B 3 4 + 5 2 4 𝑖
  • C 3 + 6 5 𝑖
  • D βˆ’ 9 1 3 βˆ’ 5 2 6 𝑖
  • E βˆ’ 1 1 8 βˆ’ 3 8 𝑖

Q7:

Simplify 4 + 𝑖 4 βˆ’ 𝑖 .

  • A 1 5 + 8 𝑖 1 7
  • B 1 7 1 5 + 8 𝑖
  • C 1 5 + 8 𝑖 1 5
  • D 1 βˆ’ 𝑖
  • E 1 7 + 8 𝑖 1 5

Q8:

Simplify ( 8 + 7 𝑖 ) ( 1 + 8 𝑖 ) ( 6 + 4 𝑖 ) .

  • A βˆ’ 1 1 3 + 3 0 9 2 6 𝑖
  • B 1 1 3 βˆ’ 3 0 9 2 6 𝑖
  • C 1 5 βˆ’ 3 0 9 1 0 𝑖
  • D βˆ’ 1 5 + 3 0 9 1 0 𝑖

Q9:

Express ( 5 + 5 𝑖 ) ( 8 βˆ’ 4 𝑖 ) 1 βˆ’ 𝑖 in the form π‘Ž + 𝑏 𝑖 .

  • A 2 0 + 4 0 𝑖
  • B βˆ’ 5 + 4 0 𝑖
  • C 6 0 + 2 0 𝑖
  • D 2 8 + 1 6 𝑖
  • E 4 0 βˆ’ 2 0 𝑖

Q10:

Simplify ( βˆ’ 3 + 2 𝑖 ) ( 3 + 3 𝑖 ) ( 4 + 𝑖 ) ( 4 + 4 𝑖 ) .

  • A βˆ’ 1 5 3 4 + 3 3 6 8 𝑖
  • B 1 5 3 4 + 3 3 6 8 𝑖
  • C 1 5 3 4 βˆ’ 3 3 6 8 𝑖
  • D βˆ’ 1 5 3 4 βˆ’ 3 3 6 8 𝑖

Q11:

Simplify βˆ’ 1 βˆ’ 9 𝑖 + 5 𝑖 βˆ’ 7 𝑖 βˆ’ 6 + 4 𝑖 βˆ’ 4 𝑖 + 2 𝑖 2 3 2 3 .

  • A 1 + 2 𝑖
  • B βˆ’ 1 + 𝑖
  • C βˆ’ 1 βˆ’ 𝑖
  • D 1 βˆ’ 2 𝑖

Q12:

Simplify βˆ’ 7 + 𝑖 + 3 𝑖 βˆ’ 6 𝑖 βˆ’ 2 βˆ’ 𝑖 βˆ’ 𝑖 βˆ’ 𝑖 2 3 2 3 .

  • A 1 0 βˆ’ 7 𝑖
  • B 4 βˆ’ 3 𝑖
  • C 4 + 3 𝑖
  • D 1 0 + 7 𝑖

Q13:

Solve the equation 𝑖 𝑧 = βˆ’ 4 + 3 𝑖 .

  • A 𝑧 = 3 + 4 𝑖
  • B 𝑧 = βˆ’ 4 + 3 𝑖
  • C 𝑧 = 3 βˆ’ 4 𝑖
  • D 𝑧 = βˆ’ 3 + 4 𝑖
  • E 𝑧 = βˆ’ 3 βˆ’ 4 𝑖

Q14:

If π‘Ž + 𝑏 𝑖 = βˆ’ 3 βˆ’ 5 𝑖 βˆ’ 3 + 5 𝑖 , is it true that π‘Ž + 𝑏 = 1 2 2 ?

  • Ano
  • Byes
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