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 Imaginary and complex numbers

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Why does i raised to an exponent change when using even numbers? You'd expect that a negative number with an even exponent to always come out positive. Can someone explain the pattern:

i^2= -1, i^4+ 1, i^6= 1, i^8= -1, i^10= 1, and so on. Why does it bounce from negative to positve? 

 Nov 18, 2014

Best Answer 

 #1
avatar+118703 
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By definition

i=√−1

Remember this is not a real number it is an imaginary number!

squares and square roots cancle each other out so

 

i2=(√−1)2=−1i4=i2×i2=−1×−1=+1i6=i4×i2=1×−1=−1i8=i6×i2=−1×−1=+1i10=i8×i2=+1×−1=−1

 

does that help you to understand?  

 Nov 19, 2014

1+0 Answers

 #1
avatar+118703 
+10
Best Answer

By definition

i=√−1

Remember this is not a real number it is an imaginary number!

squares and square roots cancle each other out so

 

i2=(√−1)2=−1i4=i2×i2=−1×−1=+1i6=i4×i2=1×−1=−1i8=i6×i2=−1×−1=+1i10=i8×i2=+1×−1=−1

 

does that help you to understand?  

Melody Nov 19, 2014

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