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Question

Find the values of x and y which satisfy the given equations (x,yR) x11+i+y11i=i.

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Solution

x11+i+y11i=c

(x1)(1i)+(y1)(1+i)(1+i)(1i)=c

xxi1+i+y+yi+ii1+1=i

x(1i)1+y(1+i)1=2i

x(1i)+y(1+i)=2+2i

x+y+i(x+y)=2+2i

By comparing real and complex part we get,

x+y=2 & yx=2

2y=4

y=2

so, x=0 & y=2

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