Correct Option: C

The given circuit:

Given that power dissipated in the 6Ω resistor is zero, it means voltage at node 1 is same as 2 (i.e., V₁ = V₂)
KCL at node 1

V1 - 20    0°	+	V1	+	V1 + V2	= 0
1		j1		6 + j8

or

V1 1 +	1	20  0°(since V1 = V2)
	j1

or

V1 = 20   0°	j	.........…(i)
	(j + 1)

Again KCL at node 2:

V2 – V1	+	V1	+	V2 – V	= 0
6 + j8		5		5

or

2V2	=	V	(since V1 = V2)
5		5

or

V2 =	V	...........(ii)
	2

From equation (i) and (ii)

20   0°	j	=	V
	j + 1		2

or

V =	2 × 20 0° × 90°
	2 × 45°

20 2 45°
Hence alternative (A) is the correct choice.