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Lesson: Purely 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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02:01

Worksheet • 20 Questions • 2 Videos

Q1:

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

Q2:

Simplify 1 7 𝑖 ( βˆ’ 5 𝑖 ) .

Q3:

Simplify ( 2 𝑖 ) ( βˆ’ 2 𝑖 ) 2 3 .

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

Q4:

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

Q5:

Simplify √ βˆ’ 6 1 .

  • A √ 6 1 𝑖
  • B 6 1 𝑖
  • C βˆ’ √ 6 1 𝑖
  • D √ 6 1
  • E βˆ’ √ 6 1

Q6:

Simplify 𝑖 βˆ’ 5 4 .

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

Q7:

Simplify 1 𝑖 βˆ’ 3 9 .

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

Q8:

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

Q9:

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 }

Q10:

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

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

Q11:

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

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

Q12:

Simplify 𝑖 2 9 .

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

Q13:

Simplify the expression 𝑖 3 .

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

Q14:

Simplify 1 𝑖 4 5 .

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

Q15:

What is the value of ( 5 𝑖 )  ?

Q16:

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

Q17:

Simplify ( 3 𝑖 ) ( βˆ’ 2 𝑖 ) 2 3 .

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

Q18:

Simplify βˆ’ 1 7 𝑖 ( βˆ’ 1 0 𝑖 ) .

Q19:

Simplify 1 𝑖 2 7 .

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

Q20:

Simplify 𝑖 2 5 .

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