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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
Hello student,Please find the answer to your question belowThe proof which you are showing is an analytical proofThese 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 graphso 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.hencei2is treated as -1.
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