Find the square root of - x2/y2 + y2/x2 + 1/2i (x/y+y/x) + 31/16 Share with your friends Share 3 Tanveer Sofi answered this The given complex number isx2y2+y2x2+12ixy+yx+3116It can be written as:x2y2+y2x2+2+12ixy+yx+3116-2=x2y2+y2x2+2+12ixy+yx-116=xy+yx2-116+12ixy+yxNow, let us assumexy+yx2-116+12ixy+yx=a+ib⇒xy+yx2-116+12ixy+yx=a2-b2+2iabOn equating real and imaginary parts, we geta2-b2=xy+yx2-116 ...........iand ab=14xy+yx ...........iiNow,a2+b22=a2-b22+4a2b2⇒a2+b2=xy+yx2+116 .............iiiSolving equations i and iii, we geta2=xy+yx2 and b2=116⇒a=±xy+yx and b=±14Now, if xy+yx is positive both a and b have same sign:xy+yx2-116+12ixy+yx =±xy+yx+14iNow, if xy+yx is negative , a and b have opposite sign:xy+yx2-116+12ixy+yx =±xy+yx-14i -2 View Full Answer
