Worksheet: Purely Imaginary Numbers

Practice

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

Q1:

Solve the equation 2 𝑥 = − 5 0 2 .

  • A 𝑥 = 5 √ 2 𝑖 , 𝑥 = − 5 √ 2 𝑖
  • B 𝑥 = 5 , 𝑥 = − 5
  • C 𝑥 = 5 √ 2 2 𝑖 , 𝑥 = − 5 √ 2 2 𝑖
  • D 𝑥 = 5 𝑖 , 𝑥 = − 5 𝑖
  • E 𝑥 = 5 2 𝑖 , 𝑥 = − 5 2 𝑖

Q2:

Simplify 1 7 𝑖 ( − 5 𝑖 ) .

Q3:

Simplify ( 2 𝑖 ) ( − 2 𝑖 ) .

  • A32
  • B 3 2 𝑖
  • C4
  • D − 3 2 𝑖
  • E − 4 𝑖

Q4:

Solve the equation 𝑥 = − 1 6 2 .

  • A 𝑥 = − 8
  • B 𝑥 = 4 , 𝑥 = − 4
  • C 𝑥 = 2 𝑖 , 𝑥 = − 2 𝑖
  • D 𝑥 = 4 𝑖 , 𝑥 = − 4 𝑖
  • E 𝑥 = 𝑖 , 𝑥 = 4

Q5:

Simplify √ − 6 1 .

  • A − √ 6 1
  • B − √ 6 1 𝑖
  • C √ 6 1
  • D √ 6 1 𝑖
  • E 6 1 𝑖

Q6:

Simplify 𝑖 .

  • A 𝑖
  • B 1
  • C − 𝑖
  • D − 1

Q7:

Simplify 1 𝑖 .

  • A − 1
  • B1
  • C 𝑖
  • D − 𝑖

Q8:

Simplify √ − 1 0 × √ − 6 .

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

Q9:

Determine the solution set of 4 𝑥 + 1 1 1 = 7 5 over the set of complex numbers.

  • A { − 3 𝑖 }
  • B { 3 𝑖 }
  • C { 0 , 3 𝑖 }
  • D { − 3 𝑖 , 3 𝑖 }

Q10:

Simplify 𝑖 , given that 𝑛 ∈ ℤ .

  • A − 1
  • B 1
  • C 𝑖
  • D − 𝑖

Q11:

Given that 𝑛 is an integer, simplify 𝑖 .

  • A − 1
  • B1
  • C − 𝑖
  • D 𝑖

Q12:

Simplify 𝑖 2 9 .

  • A − 1
  • B1
  • C − 𝑖
  • D 𝑖

Q13:

Simplify the expression 𝑖 3 .

  • A 𝑖
  • B − 1
  • C1
  • D − 𝑖

Q14:

Simplify 1 𝑖 4 5 .

  • A − 1
  • B1
  • C 𝑖
  • D − 𝑖

Q15:

What is the value of ( 5 𝑖 ) ?

Q16:

Simplify ( − 2 𝑖 ) ( 2 𝑖 ) .

  • A − 4
  • B64
  • C4
  • D − 6 4

Q17:

Simplify ( − 2 𝑖 ) ( 2 𝑖 ) .

  • A − 6 4 𝑖
  • B − 6 4
  • C − 4 𝑖
  • D64
  • E4

Q18:

Simplify − 6 𝑖 ( − 8 𝑖 ) .

Q19:

Simplify 1 𝑖 .

  • A − 1
  • B1
  • C − 𝑖
  • D 𝑖

Q20:

Simplify 𝑖 .

  • A − 1
  • B 1
  • C − 𝑖
  • D 𝑖

Q21:

Find the value of − √ − 1 4 4 .

  • A 1 2 𝑖
  • B − 1 2
  • C12
  • D − 1 2 𝑖
  • E − 1 4 4 𝑖

Q22:

What is ( 2 − 7 𝑖 ) + ( − 4 − 3 𝑖 ) 2 ?

  • A − 4 5 − 2 8 𝑖
  • B − 2 − 1 0 𝑖
  • C − 4 1 − 2 5 𝑖
  • D − 4 9 − 3 1 𝑖
  • E − 4 1 − 3 1 𝑖

Q23:

What is √ − 2 5 ?

  • A5
  • B − 5
  • C − 5 𝑖
  • D 5 𝑖
  • E 2 5 𝑖

Q24:

Find the value of ( − 1 2 8 ) .

Q25:

Simplify 3 √ − 0 . 0 6 4 𝑎 3 0 .

  • A − 0 . 0 6 4 𝑎 1 0
  • B − 0 . 4 𝑎 3 0
  • C 0 . 0 4 𝑎 1 0
  • D − 0 . 4 𝑎 1 0
  • E 0 . 4 𝑎 1 0

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