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.

  • A𝑥=5,𝑥=−5
  • B𝑥=5𝑖,𝑥=−5𝑖
  • C𝑥=5√2𝑖,𝑥=−5√2𝑖
  • D𝑥=5√22𝑖,𝑥=−5√22𝑖
  • E𝑥=52𝑖,𝑥=−52𝑖

Q2:

Simplify 17𝑖(−5𝑖).

Q3:

Simplify (2𝑖)(−2𝑖).

  • A32
  • B−32𝑖
  • C4
  • D−4𝑖
  • E32𝑖

Q4:

Solve the equation 𝑥=−16.

  • A𝑥=−8
  • B𝑥=2𝑖,𝑥=−2𝑖
  • C𝑥=4𝑖,𝑥=−4𝑖
  • D𝑥=𝑖,𝑥=4
  • E𝑥=4,𝑥=−4

Q5:

Simplify √−61.

  • A−√61𝑖
  • B−√61
  • C61𝑖
  • D√61𝑖
  • E√61

Q6:

Simplify 𝑖.

  • A−𝑖
  • B−1
  • C𝑖
  • D1

Q7:

Simplify 1𝑖.

  • A−1
  • B−𝑖
  • C1
  • D𝑖

Q8:

Simplify √−10×√−6.

  • A−4
  • B2√15𝑖
  • C−2√15𝑖
  • D2√15
  • E−2√15

Q9:

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

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

Q10:

Simplify 𝑖, given that 𝑛∈ℤ.

  • A−1
  • B𝑖
  • C1
  • D−𝑖

Q11:

Given that 𝑛 is an integer, simplify 𝑖.

  • A−1
  • B𝑖
  • C−𝑖
  • D1

Q12:

Simplify 𝑖.

  • A1
  • B−𝑖
  • C−1
  • D𝑖

Q13:

Simplify the expression 𝑖.

  • A−1
  • B−𝑖
  • C1
  • D𝑖

Q14:

Simplify 1𝑖.

  • A−𝑖
  • B−1
  • C𝑖
  • D1

Q15:

What is the value of (5𝑖)?

Q16:

Simplify (−2𝑖)(2𝑖).

  • A−64
  • B−4
  • C4
  • D64

Q17:

Simplify (−2𝑖)(2𝑖).

  • A−64𝑖
  • B64
  • C−4𝑖
  • D4
  • E−64

Q18:

Simplify −6𝑖(−8𝑖).

Q19:

Simplify 1𝑖.

  • A−1
  • B𝑖
  • C−𝑖
  • D1

Q20:

Simplify 𝑖.

  • A−1
  • B−𝑖
  • C𝑖
  • D1

Q21:

Find the value of −√−144.

  • A−12𝑖
  • B−144𝑖
  • C12
  • D−12
  • E12𝑖

Q22:

What is √−25?

  • A25𝑖
  • B−5𝑖
  • C−5
  • D5𝑖
  • E5

Q23:

What is the value of 𝑖?

  • A𝑖
  • B−1
  • C−𝑖
  • D1

Q24:

What is the value of 𝑖?

Q25:

What is the value of 3𝑖?

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