Q23 of 153 Page 13

Solve the equation |z| = z + 1 + 2i.

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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