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CBSE Class 12-science Answered

what is square root of  i ? 
Asked by sachinjadhav5168 | 02 Apr, 2019, 10:51: AM
answered-by-expert Expert Answer
let space square space root space of space straight i space be space straight x plus iy
square root of straight i equals straight x plus iy
straight i equals open parentheses straight x squared minus straight y squared close parentheses plus 2 xyi
comparing
straight x squared minus straight y squared equals 0.....1
2 xy equals 1......2
now comma
straight x squared plus straight y squared equals open parentheses straight x squared minus straight y squared close parentheses plus 4 straight x squared straight y squared
straight x squared plus straight y squared equals 1.....3
straight x squared equals 1 half
straight x equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction space straight y equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction
from space 2 comma space we space infer space that space both space straight x space and space straight y space should space have space same space sign
square space root space is space
fraction numerator 1 over denominator square root of 2 end fraction plus straight i fraction numerator 1 over denominator square root of 2 end fraction
Or
minus fraction numerator 1 over denominator square root of 2 end fraction minus straight i fraction numerator 1 over denominator square root of 2 end fraction
Answered by Arun | 02 Apr, 2019, 03:12: PM
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