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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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