Question

2. If z = x + iy and
Iz-1-il+ 4/ 3|z-1-i|-2
· = 1, show that x2 + y2 - 2x - 2y = 7.​

Answer 1

Answer:

hello

Step-by-step explanation:

3∣z−1−i∣−2

∣z−1−i∣+4

=1

Put z=x+yi

3∣x+iy−1−i∣−2

∣x+iy−1−i∣+4

=1

3∣(x−1)+i(y−1)−2

∣(x−1)+i(y−1)∣+4

=1

3

(x−1)

2

+(y−1)

2

−2

(x−1)

2

+(y−1)

2

+4

=1

(x−1)

2

+(y+1)

2

+4

=3

(x−1)

2

+(y−1)

2

−2

2

(x−1)

2

+(y−1)

2

=6

(x−1)

2

+(y−1)

2

=3

(x

2

+1−2x+y

2

+1−2y)

=9

x

2

+y

2

−2x−2y−7=0 Hence proved