Q. 2

Write the values of the square root of –i.

Answer :


Squaring both side


-i = (x + iy)2


= (x2-y2)+2ixy


x2-y2 = 0


2xy = -1


As we know all that,


(x2+y2)2 = (x2-y2)2+4x2y2


(x2+y2)2 = 0+1


(x2+y2)2 = 1


x2+y2 = 1


X2-y2 = 0 ……………………. (1)


x2+y2 = 1 ……………….(2)


From (1)


x2 = y2…………….(3)


2x2 = 1 (because x2 = y2)


2xy = -1


it means xy<0


Either x<0 , y > 0


Or x>0, y<0


X and y have different sign




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