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Imaginary Numbers

Imaginary numbers are based around mathematical number i  which is the square root of  - 1.
  • i is defined to be
  • i has the following important property
    Examples
    • Imaginary Number Example Two

How to simplify i to any given power:
  • Since i4 is the number 1 we can apply the following formula to reduce i to any power
      ik = ir
      Where r = the remainder of k÷4
      Examples
    • i9
      • Step 1. 9 ÷ 4 has a remainder of 1
      • Step 2. i9 = i1
    • i22
      • Step 1. 22÷ 4 has a remainder of 2
      • Step 2. i22 = i2
    • i103
      • Step 1. 103 ÷ 4 has a remainder of 3
      • Step 2. i103 = i3 = -i

Imaginary Number Calculator and Solver

Type any negative number into the calculator below and hit 'reduce' to reduce the imaginary number to simplest radical form.
More Math Warehouse Calculators

Imaginary Numbers
Practice Problems
Simplify the imaginary numbers below:

Problem 1)
 answer  



Problem 2)
 answer  

Problem 3)
 answer  

Problem  4) 
 answer  

Problem 5)
 answer  

Problem 6)
 answer  

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