another complex numbers question (1 Viewer)

[Hermes1]

A complex number z is such that arg(z+2) = pi/6 and arg(z-2) = 2pi/3
find z, expressing your answer in x+iy form

 

[Hermes1]

I think ive got it can someone verify:
arg(z-2) - arg(z+2) = pi/2
therefore z-2/z+2 = i
and then you let z = x+iy
and i got an answer of -2 and 2i,
but only 2i is correct

is that right?

 

[jyu]

A complex number z is such that arg(z+2) = pi/6 and arg(z-2) = 2pi/3
find z, expressing your answer in x+iy form

z=1+(sqrt3)i

 

[xV1P3R]

z=1+(sqrt3)i

This. I think the problem with your solution is this step:

arg(z-2) - arg(z+2) = pi/2
therefore z-2/z+2 = i

You got rid of the args by 'tan'ing both sides taking tan(pi/2) = i

 

[jyu]

are you referring to my answer?

 

[xV1P3R]

oh no. arj1's solution

 

[ZachBC_94]

Complex numbers are always so much easier if you use the Argand Diagram, particularly these questions.

Here's a starter: