Q. If `z=x+iy` satisfies the equation `arg(z-2) = arg(2z+3i)` then `3x-4y` is equal to:-

A) 5

B) -3

C) 6

D) 7

### 1 Answer | Add Yours

The complex number z = x + i*y. It is given that arg(z - 2) = arg(2z + 3i).

arg(z - 2) = `tan^-1(y/(x-2))`

arg(2z + 3i) = `tan^-1((2y+3)/(2x))`

`tan^-1(y/(x-2))` = `tan^-1((2y+3)/(2x))`

=> `y/(x - 2) = (2y + 3)/(2x)`

=> 2xy = (2y+3)(x-2)

=> 2xy = 2xy+3x-4y-6

=> 3x - 4y = 6

**The correct answer is option C.**

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