Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If |z + 1| = z + 2 (1 + i), then find z

If |z + 1| = z + 2 (1 + i), then find z

Answers (1)

We have |z + 1| = z + 2 (1 + i)

Substituting z=x+iy we get x+iy+1=x+iy+2i+1

|z|= \sqrt{(x^2+y^2 ) }=\sqrt{(x+1)^2+y^2 } = (x+2)+i(y+2)

Comparing real and imaginary parts, \sqrt{(x+1)^2+y^2 } = (x+2)

and 0=y+2 ;y=-2

Substituting the value of y in  \sqrt{(x+1)^2+y^2 } = (x+2)

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

x^2+2x+1+4=x^2+4x+4

2x=1

Hence, x=\frac{1}{2}

Thus, z=x+iy=\frac{1}{2}-2i

 

 

 

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question