Question

Q19. If z = x + iy and Real part of +2 = 4, then show that x² + y2 - 3x + 2 = 0​

Answer 1

Answer:

Let z=x+iy

∴

(z−i)

z+i

=

x+iy−i

x+iy+i

=

(x−i(1−y))

(x+i(y+1))

×

(x+i(1−y))

(x+i(1−y))

=

x

2

+(1−y)

2

x

2

+(y

2

−1)+2ix

Since,

z−i

z+i

should be purely imaginary

∴Re(

z−i

z+i

)=0

⟹

x

2

+(1−y)

2

x

2

+(y

2

−1)

=0

⟹x

2

+y

2

−1=0

⟹x

2

+y

2

=1 which is the equation of a circle

Hence, (x,y) lie on a circle.