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Lesson: Operations with Pure Imaginary Numbers

In this lesson, we will learn how to evaluate, simplify, and multiply pure imaginary numbers and solve equations over the set of pure imaginary numbers.

Sample Question Videos

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Worksheet • 19 Questions • 2 Videos

Q1:

Simplify ( 2 𝑖 ) ( 3 𝑖 ) 3 2 .

  • A 7 2 𝑖
  • B 6 𝑖
  • C βˆ’ 7 2 𝑖
  • D βˆ’ 6
  • E βˆ’ 7 2

Q2:

Simplify ( 2 𝑖 ) ( βˆ’ 2 𝑖 ) 2 3 .

  • A βˆ’ 3 2 𝑖
  • B βˆ’ 4 𝑖
  • C 3 2 𝑖
  • D4
  • E32

Q3:

Simplify ( 3 𝑖 ) ( βˆ’ 2 𝑖 ) 2 3 .

  • A βˆ’ 7 2 𝑖
  • B βˆ’ 6 𝑖
  • C 7 2 𝑖
  • D6
  • E72

Q4:

Solve the equation 2 π‘₯ = βˆ’ 5 0 2 .

  • A π‘₯ = 5 𝑖 , π‘₯ = βˆ’ 5 𝑖
  • B π‘₯ = 5 2 𝑖 , π‘₯ = βˆ’ 5 2 𝑖
  • C π‘₯ = 5 , π‘₯ = βˆ’ 5
  • D π‘₯ = 5 √ 2 2 𝑖 , π‘₯ = βˆ’ 5 √ 2 2 𝑖
  • E π‘₯ = 5 √ 2 𝑖 , π‘₯ = βˆ’ 5 √ 2 𝑖

Q5:

Simplify 1 7 𝑖 ( βˆ’ 5 𝑖 ) .

Q6:

Simplify βˆ’ 1 7 𝑖 ( βˆ’ 1 0 𝑖 ) .

Q7:

Simplify the expression 𝑖 3 .

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

Q8:

Determine the solution set of 4 π‘₯ + 1 1 1 = 7 5 2 over the set of complex numbers.

  • A { βˆ’ 3 𝑖 , 3 𝑖 }
  • B { 3 𝑖 }
  • C { 0 , 3 𝑖 }
  • D { βˆ’ 3 𝑖 }

Q9:

Simplify 1 𝑖 βˆ’ 3 9 .

  • A βˆ’ 𝑖
  • B1
  • C 𝑖
  • D βˆ’ 1

Q10:

Simplify 1 𝑖 2 7 .

  • A 𝑖
  • B1
  • C βˆ’ 𝑖
  • D βˆ’ 1

Q11:

Simplify 1 𝑖 4 5 .

  • A βˆ’ 𝑖
  • B1
  • C 𝑖
  • D βˆ’ 1

Q12:

Solve the equation π‘₯ = βˆ’ 1 6 2 .

  • A π‘₯ = 4 𝑖 , π‘₯ = βˆ’ 4 𝑖
  • B π‘₯ = 𝑖 , π‘₯ = 4
  • C π‘₯ = 4 , π‘₯ = βˆ’ 4
  • D π‘₯ = 2 𝑖 , π‘₯ = βˆ’ 2 𝑖
  • E π‘₯ = βˆ’ 8

Q13:

Simplify 𝑖 βˆ’ 5 4 .

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

Q14:

Simplify 𝑖 2 5 .

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

Q15:

Simplify 𝑖 4 0 .

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

Q16:

Simplify 𝑖 1 2 𝑛 + 3 9 , given that 𝑛 ∈ β„€ + .

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

Q17:

Given that 𝑛 is an integer, simplify 𝑖 1 6 𝑛 βˆ’ 3 5 .

  • A 𝑖
  • B1
  • C βˆ’ 𝑖
  • D βˆ’ 1

Q18:

Simplify √ βˆ’ 1 0 Γ— √ βˆ’ 6 .

  • A βˆ’ 2 √ 1 5
  • B βˆ’ 2 √ 1 5 𝑖
  • C 2 √ 1 5 𝑖
  • D βˆ’ 4
  • E 2 √ 1 5

Q19:

Simplify 𝑖 2 9 .

  • A 𝑖
  • B1
  • C βˆ’ 𝑖
  • D βˆ’ 1
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