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Question

If  z+x+iy then (z)=x2+y2 z1=2i,z2=1+i, find z1+z2+1z1z2+i.


Solution

Ifz+x+iy then (z)=x2+y2We have,z1=2i,z2=1+iz1+z2=2i+1+i=3And z1z2=2i1i=12iz1+z2+1z1z2+i=3+112i+i=41i=41i×1+i1+i=4(1+i)12+12=4(1+i)2=2(1+i) z1+z2+1z1z2+i=|2(1+i)|=|2||1+i|     ( |z1z2|=|z1|×|z2|)=2×12+12=2×2=22


Mathematics
RD Sharma
Standard XI

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