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how i^(2) = -1 let i = (-1)^(1/2) =(3-4)^(1/2) = {[(3-4)^(2)]^(0.5)}^(0.5) ={[(9+16-24)^(0.5)]^(0.5) = {[(1)^(0.5)]^(0.5) =(1)^0.5 =1....... then why cant we write i=1 ? then all imaginary number concept will be vanished

how  i^(2) = -1 


let i = (-1)^(1/2)


       =(3-4)^(1/2)


        = {[(3-4)^(2)]^(0.5)}^(0.5)


         ={[(9+16-24)^(0.5)]^(0.5)


         = {[(1)^(0.5)]^(0.5)


         =(1)^0.5


         =1.......


then why cant we write i=1 ? then all imaginary number concept will be vanished

Grade:8

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
The proof which you are showing is an analytical proof
These kind of proofs can be done in mathematics to show 2=1,2=5 etc,,,which are actually not true
‘i’ actually represents a rotation of 90 degrees that is why we represent a complex number as (x,y) while plotting on graph
so i2means i multiplied by i which makes the rotation 180 degrees so on a graph paper you can see that this 180 degree rotation makes magnitude negative.hence
i2is treated as -1.

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