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Question

If x+iy=a+ibaib, prove that x2+y2=1


Solution

x+iy=a+ibaib ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(x+iy)=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(a+ibaib)     (on taking conjugate both sides) xiy=(¯¯¯¯¯¯¯¯¯¯a+ib)(¯¯¯¯¯¯¯¯¯¯aib)     ( (¯¯¯¯¯¯z1z2)=¯¯¯¯z1¯¯¯¯z2)=aiba+ib (x+iy)(xiy)=a+ibaib×aiba+ib x2+y2=1proved.


Mathematics
RD Sharma
Standard XI

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