Question

22. If *
(2 Points)
Z = (3i - 1)2 then z = ?​

Answer 1

Step-by-step explanation:

ANSWER

Let

z=x+iy

∣z−2i∣=2

2

(x)

2

+(y−2)

2

=8

Hence

x=2

2

cosθ

y−2=2

2

sinθ

y=2+2

2

sinθ

Hence

z+2

z−2

=

(2

2

cosθ+2)+i(2+2

2

sinθ)

(2

2

cosθ−2)+i(2+2

2

sinθ)

=

(2

2

cosθ−2)

2

+(2+2

2

sinθ)

2

(2

2

cosθ−2)+i(2+2

2

sinθ).(2

2

cosθ+2)−i(2+2

2

sinθ)

λ=

(2

2

cosθ−2)

2

+(2+2

2

sinθ)

2

(8+8

2

sinθ)+i(8+8

2

sinθ)

Therefore,

Re(λ)=Im(λ)

⇒arg(λ)=

4

π

Hence, option 'B' is correct.