Answer :

Given:


|z|=z+1+2i


Let us assume z=x+iy


|x+iy|=x+iy+1+2i



Equating Real and Imaginary parts on both sides we get


y+2=0


y=-2-----------------------(1)



x2+(-2)2=(x+1)2


x2+4=x2+2x+1


2x=3



.


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