Worksheet: Pure Imaginary Numbers

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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 2𝑥=−50.

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

Q2:

Simplify 17𝑖(−5𝑖).

Q3:

Simplify (2𝑖)(−2𝑖).

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

Q4:

Solve the equation 𝑥=−16.

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

Q5:

Simplify √−61.

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

Q6:

Simplify 𝑖.

  • A − 𝑖
  • B − 1
  • C 𝑖
  • D1

Q7:

Simplify 1𝑖.

  • A 𝑖
  • B1
  • C − 𝑖
  • D − 1

Q8:

Simplify √−10×√−6.

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

Q9:

Determine the solution set of 4𝑥+111=75 over the set of complex numbers.

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

Q10:

Simplify 𝑖, given that 𝑛∈ℤ.

  • A − 1
  • B 𝑖
  • C1
  • D − 𝑖

Q11:

Given that 𝑛 is an integer, simplify 𝑖.

  • A − 1
  • B 𝑖
  • C − 𝑖
  • D1

Q12:

Simplify 𝑖.

  • A1
  • B − 𝑖
  • C − 1
  • D 𝑖

Q13:

Simplify the expression 𝑖.

  • A − 1
  • B − 𝑖
  • C1
  • D 𝑖

Q14:

Simplify 1𝑖.

  • A − 𝑖
  • B − 1
  • C 𝑖
  • D1

Q15:

What is the value of (5𝑖)?

Q16:

Simplify (−2𝑖)(2𝑖).

  • A − 6 4
  • B − 4
  • C4
  • D64

Q17:

Simplify (−2𝑖)(2𝑖).

  • A − 6 4 𝑖
  • B64
  • C − 4 𝑖
  • D4
  • E − 6 4

Q18:

Simplify −6𝑖(−8𝑖).

Q19:

Simplify 1𝑖.

  • A − 𝑖
  • B1
  • C − 1
  • D 𝑖

Q20:

Simplify 𝑖.

  • A − 1
  • B − 𝑖
  • C 𝑖
  • D1

Q21:

Find the value of −√−144.

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

Q22:

What is √−25?

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

Q23:

What is the value of 𝑖?

  • A 𝑖
  • B − 1
  • C − 𝑖
  • D1

Q24:

What is the value of 𝑖?

Q25:

What is the value of 3𝑖?

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