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Worksheet: Purely Imaginary Numbers

In this worksheet, we will practice evaluating, simplifying, and multiplying pure imaginary numbers and solving equations over the set of pure imaginary numbers.

Q1:

Simplify ( 2 𝑖 ) ( 3 𝑖 ) 3 2 .

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

Q2:

Simplify ( 2 𝑖 ) ( βˆ’ 2 𝑖 ) 2 3 .

  • A32
  • B 3 2 𝑖
  • C4
  • D βˆ’ 3 2 𝑖
  • E βˆ’ 4 𝑖

Q3:

Simplify ( 3 𝑖 ) ( βˆ’ 2 𝑖 ) 2 3 .

  • A72
  • B 7 2 𝑖
  • C6
  • D βˆ’ 7 2 𝑖
  • E βˆ’ 6 𝑖

Q4:

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

  • A π‘₯ = 5 √ 2 𝑖 , π‘₯ = βˆ’ 5 √ 2 𝑖
  • B π‘₯ = 5 , π‘₯ = βˆ’ 5
  • C π‘₯ = 5 √ 2 2 𝑖 , π‘₯ = βˆ’ 5 √ 2 2 𝑖
  • D π‘₯ = 5 𝑖 , π‘₯ = βˆ’ 5 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 𝑖
  • B βˆ’ 1
  • C1
  • D βˆ’ 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 }
  • B { 3 𝑖 }
  • C { 0 , 3 𝑖 }
  • D { βˆ’ 3 𝑖 , 3 𝑖 }

Q9:

Simplify 1 𝑖 βˆ’ 3 9 .

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

Q10:

Simplify 1 𝑖 2 7 .

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

Q11:

Simplify 1 𝑖 4 5 .

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

Q12:

Solve the equation π‘₯ = βˆ’ 1 6 2 .

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

Q13:

Simplify 𝑖 βˆ’ 5 4 .

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

Q14:

Simplify 𝑖 2 5 .

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

Q15:

Simplify 𝑖 4 0 .

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

Q16:

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

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

Q17:

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

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

Q18:

Simplify √ βˆ’ 1 0 Γ— √ βˆ’ 6 .

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

Q19:

Simplify 𝑖 2 9 .

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

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