Please answer fast! 7 If z is complex number satisfying the relation z + 1 - Maths - Complex Numbers and Quadratic Equations

Question

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7       I f   z   i s   c o m p l e x
  n u m b e r   s a t i s f y i n g   t h e   r
e l a t i o n   z   +   1   =   z   +
  2 ( 1   +   i ) ,   t h e n   z   i
s   ( A )       1 2   1   +   4
i                  
                 
                 
                 
                ( B )
        1 2   3   +   4 i ( C )
          1 2   1   -   4 i
                 
                 
                 
                 
              ( D )  
  n o n e   o f   t h e s e

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We havez+1=z+21+iLet z=x+iy⇒x+iy+1=x+iy+21+i⇒x+1+iy=x+2+iy+2⇒x+12+y2=x+2+iy+2Compare real and imaginary partsy+2=0⇒y=-2x+12+y2=x+2⇒x+12+4=x+2⇒x2+1+2x+4=x2+4+4x⇒x=12Hencex+iy=12-2i=121-4i

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Please answer fast! 7 . I f z i s c o m p l e x n u m b e r s a t i s f y i n g t h e r e l a t i o n z + 1 = z + 2 ( 1 + i ) , t h e n z i s ( A ) 1 2 1 + 4 i ( B ) 1 2 3 + 4 i ( C ) 1 2 1 - 4 i ( D ) n o n e o f t h e s e

Please answer fast!

$7 . I f z i s c o m p l e x n u m b e r s a t i s f y i n g t h e r e l a t i o n |z + 1| = z + 2 (1 + i), t h e n z i s (A) \frac{1}{2} (1 + 4 i) (B) \frac{1}{2} (3 + 4 i) (C) \frac{1}{2} (1 - 4 i) (D) n o n e o f t h e s e$