Worksheet: nth Root of Negative Real Numbers

In this worksheet, we will practice using the pure imaginary numbers to find the nth root when n is even and when it is odd.

Q1:

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

Q2:

Find the value of 1 4 4 .

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

Q3:

What is 2 5 ?

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

Q4:

Find the value of ( 1 2 8 ) .

Q5:

Is the cube root of a negative number positive or negative?

  • A negative
  • B positive

Q6:

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

Q7:

Simplify 3 0 . 0 0 0 0 6 4 𝑎 7 2 .

  • A 0 . 0 0 0 0 6 4 𝑎 2 4
  • B 0 . 0 4 𝑎 7 2
  • C 0 . 0 0 4 𝑎 2 4
  • D 0 . 0 4 𝑎 2 4
  • E 0 . 0 4 𝑎 2 4

Q8:

Find the value of ( 1 , 0 0 0 ) .

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